What is the least number when divided by 8 12 15 and 20 leaves in each case a remainder of 5?

LCM of 8, 12, 15, and 20 is the smallest number among all common multiples of 8, 12, 15, and 20. The first few multiples of 8, 12, 15, and 20 are (8, 16, 24, 32, 40 . . .), (12, 24, 36, 48, 60 . . .), (15, 30, 45, 60, 75 . . .), and (20, 40, 60, 80, 100 . . .) respectively. There are 3 commonly used methods to find LCM of 8, 12, 15, 20 - by division method, by prime factorization, and by listing multiples.

Nội dung chính Show

  • What is the LCM of 8, 12, 15, and 20?
  • Methods to Find LCM of 8, 12, 15, and 20
  • LCM of 8, 12, 15, and 20 by Prime Factorization
  • LCM of 8, 12, 15, and 20 by Division Method
  • LCM of 8, 12, 15, and 20 by Listing Multiples
  • FAQs on LCM of 8, 12, 15, and 20
  • What is the LCM of 8, 12, 15, and 20?
  • How to Find the LCM of 8, 12, 15, and 20 by Prime Factorization?
  • What are the Methods to Find LCM of 8, 12, 15, 20?
  • Which of the following is the LCM of 8, 12, 15, and 20? 105, 120, 12, 50
  • What is the least number which when divided by 8 12?
  • What is the LCM of 12 and 15?
  • What is the smallest number which is a perfect square and is divisible by 16 20 and 24?
  • What is the least number when divided by 8 12 and 16 leaves 3 as remainder in each case but divided by 7 leaves no remainder?
  • What is the LCM of 12 and 8?

Nội dung chính

  • What is the LCM of 8, 12, 15, and 20?
  • Methods to Find LCM of 8, 12, 15, and 20
  • LCM of 8, 12, 15, and 20 by Prime Factorization
  • LCM of 8, 12, 15, and 20 by Division Method
  • LCM of 8, 12, 15, and 20 by Listing Multiples
  • FAQs on LCM of 8, 12, 15, and 20
  • What is the LCM of 8, 12, 15, and 20?
  • How to Find the LCM of 8, 12, 15, and 20 by Prime Factorization?
  • What are the Methods to Find LCM of 8, 12, 15, 20?
  • Which of the following is the LCM of 8, 12, 15, and 20? 105, 120, 12, 50
  • What is the least number which when divided by 8 12 15 and 20 leaves?
  • What is the least number which when divided by 8 12 15 and 20 leaves in each case a remainder of 57?
  • What is the smallest number which when divided by 8 12 20 or 25 leaves a remainder 5 in each case?
  • What is the least number which when divided by 8 12 15 and 18 leaves remainder 5 9 12 and 15 respectively?

What is the LCM of 8, 12, 15, and 20?

Answer: LCM of 8, 12, 15, and 20 is 120.

What is the least number when divided by 8 12 15 and 20 leaves in each case a remainder of 5?

Explanation:

The LCM of four non-zero integers, a(8), b(12), c(15), and d(20), is the smallest positive integer m(120) that is divisible by a(8), b(12), c(15), and d(20) without any remainder.

Methods to Find LCM of 8, 12, 15, and 20

The methods to find the LCM of 8, 12, 15, and 20 are explained below.

  • By Prime Factorization Method
  • By Division Method
  • By Listing Multiples

LCM of 8, 12, 15, and 20 by Prime Factorization

Prime factorization of 8, 12, 15, and 20 is (2 × 2 × 2) = 23, (2 × 2 × 3) = 22 × 31, (3 × 5) = 31 × 51, and (2 × 2 × 5) = 22 × 51 respectively. LCM of 8, 12, 15, and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 31 × 51 = 120.
Hence, the LCM of 8, 12, 15, and 20 by prime factorization is 120.

LCM of 8, 12, 15, and 20 by Division Method

To calculate the LCM of 8, 12, 15, and 20 by the division method, we will divide the numbers(8, 12, 15, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 8, 12, 15, and 20.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8, 12, 15, and 20. Write this prime number(2) on the left of the given numbers(8, 12, 15, and 20), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (8, 12, 15, 20) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
  • Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 8, 12, 15, and 20 is the product of all prime numbers on the left, i.e. LCM(8, 12, 15, 20) by division method = 2 × 2 × 2 × 3 × 5 = 120.

LCM of 8, 12, 15, and 20 by Listing Multiples

To calculate the LCM of 8, 12, 15, 20 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 8 (8, 16, 24, 32, 40 . . .), 12 (12, 24, 36, 48, 60 . . .), 15 (15, 30, 45, 60, 75 . . .), and 20 (20, 40, 60, 80, 100 . . .).
  • Step 2: The common multiples from the multiples of 8, 12, 15, and 20 are 120, 240, . . .
  • Step 3: The smallest common multiple of 8, 12, 15, and 20 is 120.

∴ The least common multiple of 8, 12, 15, and 20 = 120.

☛ Also Check:

  • LCM of 13 and 11 - 143
  • LCM of 14 and 28 - 28
  • LCM of 108 and 144 - 432
  • LCM of 2, 3, 4, 5, and 6 - 60
  • LCM of 3, 4 and 6 - 12
  • LCM of 5, 10, 15 and 20 - 60
  • LCM of 36, 48 and 72 - 144

FAQs on LCM of 8, 12, 15, and 20

What is the LCM of 8, 12, 15, and 20?

The LCM of 8, 12, 15, and 20 is 120. To find the LCM (least common multiple) of 8, 12, 15, and 20, we need to find the multiples of 8, 12, 15, and 20 (multiples of 8 = 8, 16, 24, 32 . . . . 120 . . . . ; multiples of 12 = 12, 24, 36, 48 . . . . 120 . . . . ; multiples of 15 = 15, 30, 45, 60 . . . . 120 . . . . ; multiples of 20 = 20, 40, 60, 80, 120 . . . .) and choose the smallest multiple that is exactly divisible by 8, 12, 15, and 20, i.e., 120.

How to Find the LCM of 8, 12, 15, and 20 by Prime Factorization?

To find the LCM of 8, 12, 15, and 20 using prime factorization, we will find the prime factors, (8 = 23), (12 = 22 × 31), (15 = 31 × 51), and (20 = 22 × 51). LCM of 8, 12, 15, and 20 is the product of prime factors raised to their respective highest exponent among the numbers 8, 12, 15, and 20.
⇒ LCM of 8, 12, 15, 20 = 23 × 31 × 51 = 120.

What are the Methods to Find LCM of 8, 12, 15, 20?

The commonly used methods to find the LCM of 8, 12, 15, 20 are:

  • Prime Factorization Method
  • Listing Multiples
  • Division Method

Which of the following is the LCM of 8, 12, 15, and 20? 105, 120, 12, 50

The value of LCM of 8, 12, 15, 20 is the smallest common multiple of 8, 12, 15, and 20. The number satisfying the given condition is 120.

Example 2: Find the smallest number which when divided by 8, 12, 15, and 20 leaves 6 as the remainder in each case. ⇒ The required number = 120 + 6 = 126.

Detailed Solution. ∴ Required least such number is 544.

The smallest number will be 600+5 = 605. Hence, the smallest number when divided by 8, 12, 20, and 25 will leave a remainder of 5 is 605.

so, answer is 125.

Answer: LCM of 8, 12, 15, and 20 is 120.

Similarly, What is the least number which when divided by 8 12 15 and 20 leaves in each case a remainder of 5 *? Answer is 845

With the addition of 5 in the LCM we get the Answer as 845, as desired number.

What is the LCM of 8 and 12? The first multiple that 8 and 12 have in common is 24. Notice that 48 is also a common multiple; however, 24 is the smallest number that they have in common. This makes it the least common multiple.

What is the smallest perfect square divisible by 8 12 15? 3600 is the right answer.

Secondly What is the least number that is exactly divisible by 8 and 12? Answer: the smallest number which is divisible by 8 and 12 is 24.

What is the least number which when divided by 8 12?

Step-by-step explanation:

44 is the least number when divided by 8,12,20.

then What is the number which when divided by 8 12 and 15 leaves a remainder 3 in each case? so, answer is 125.

What is the HCF of 8/12 and 20? As you can see when you list out the factors of each number, 4 is the greatest number that 8, 12, and 20 divides into.

What is the LCM of 12 and 15?

Answer: LCM of 12 and 15 is 60.

What is the LCM of 15 and 20? The smallest number to appear on both lists is 60, so 60 is the least common multiple of 15 and 20.

How do you find the LCM?

Find the least common multiple (LCM) of two numbers by listing multiples

  1. List the first several multiples of each number.
  2. Look for multiples common to both lists. …
  3. Look for the smallest number that is common to both lists.
  4. This number is the LCM.

What is the least number which when divided by 8 9 12 and 15 leaves the same remainder 1 in each case? Detailed Solution

The least number which is completely divisible by 8, 9, 12 and 15 will be the LCM of these numbers. ∴ The least number which when divided by 8, 9, 12 and 15, leaves the remainder 1 will be 360 + 1 = 361.

What is the smallest number which is a perfect square and is divisible by 16 20 and 24?

∴ The least number which is a perfect square and is divisible by each of the numbers 16, 20 and 24 is 3600.

Which of the following numbers is the smallest perfect square that is multiple of 8 12 and 15?

R D Sharma – Mathematics 9

Let us multiply 2, 3 and 5 , we get a grouped in pairs of equal factors. Now 3600 is perfect square that is divisible by 6, 8, 12, and 15.

What will be the least number which when divided by 8 12 15 and 18 leaves a remainder of 3 in each case? Answer: 8-3=5. 12-3=9. 15-3=12.

How do you solve for LCM? Find the LCM using the prime factors method

  1. Find the prime factorization of each number.
  2. Write each number as a product of primes, matching primes vertically when possible.
  3. Bring down the primes in each column.
  4. Multiply the factors to get the LCM.

What is the least number when divided by 8 12 and 16 leaves 3 as remainder in each case but divided by 7 leaves no remainder?

So the ans. is 147.

What is the least number which when divided by 8 12 16? The least number which when divided by 8, 12, 16, and 24 leave a remainder of 4 in each case is: 64.

What is the smallest number which when divided by 12 15 18 and 27 leaves remainder of 8 11 14 and 23 respectively?

Originally Answered: What is the smallest number, which when divided by 12, 15, 18, and 27, leaves as a remainder 8, 11, 14 and 23 respectively? The answer is 536.

What is the HCF 15 and 20? Answer: HCF of 15 and 20 is 5.

What is the LCM of 12 and 8?

The least common multiple of 8 and 12 is 24.

Whats the HCF of 12 and 8? The HCF of 8 and 12 is 4. To calculate the HCF (Highest Common Factor) of 8 and 12, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the highest factor that exactly divides both 8 and 12, i.e., 4.

What is the least number which when divided by 8 12 15 and 20 leaves?

Therefore, the LCM of 8, 12, 15, and 20 is 120. Example 2: Find the smallest number which when divided by 8, 12, 15, and 20 leaves 6 as the remainder in each case. ⇒ The required number = 120 + 6 = 126.

What is the least number which when divided by 8 9 12 15 leaves a remainder 1 in each case?

The least number which is completely divisible by 8, 9, 12 and 15 will be the LCM of these numbers. ∴ The least number which when divided by 8, 9, 12 and 15, leaves the remainder 1 will be 360 + 1 = 361.

What is the least number which when divided by 8 12 15 and 18 leaves remainder 5 9 12 and 15 respectively?

so, answer is 125.

What is the least number which when divided by 12 15 20 leaves remainder 4?

∴ Required least such number is 544.