LCM of 8 and 56

LCM of 8 and 56 is the smallest number among all common multiples of 8 and 56. The first few multiples of 8 and 56 are (8, 16, 24, 32, 40, 48, 56, . . . ) and (56, 112, 168, 224, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 56 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 8 and 56 is 56.

Explanation:

The LCM of two non-zero integers, x(8) and y(56), is the smallest positive integer m(56) that is divisible by both x(8) and y(56) without any remainder.

The methods to find the LCM of 8 and 56 are explained below.

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

LCM of 8 and 56 by Prime Factorization

Prime factorization of 8 and 56 is (2 × 2 × 2) = 2³ and (2 × 2 × 2 × 7) = 2³ × 7¹ respectively. LCM of 8 and 56 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 7¹ = 56.
Hence, the LCM of 8 and 56 by prime factorization is 56.

LCM of 8 and 56 by Listing Multiples

To calculate the LCM of 8 and 56 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, 48, 56, . . . ) and 56 (56, 112, 168, 224, . . . . )
• Step 2: The common multiples from the multiples of 8 and 56 are 56, 112, . . .
• Step 3: The smallest common multiple of 8 and 56 is 56.

∴ The least common multiple of 8 and 56 = 56.

LCM of 8 and 56 by Division Method

To calculate the LCM of 8 and 56 by the division method, we will divide the numbers(8, 56) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 56.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 56. Write this prime number(2) on the left of the given numbers(8 and 56), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 56) 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 and 56 is the product of all prime numbers on the left, i.e. LCM(8, 56) by division method = 2 × 2 × 2 × 7 = 56.

☛ Also Check:

• LCM of 5 and 8 - 40
• LCM of 9 and 16 - 144
• LCM of 4 and 12 - 12
• LCM of 4 and 24 - 24
• LCM of 30, 36 and 40 - 360
• LCM of 4 and 7 - 28
• LCM of 9 and 18 - 18

FAQs on LCM of 8 and 56

What is the LCM of 8 and 56?

The LCM of 8 and 56 is 56. To find the LCM (least common multiple) of 8 and 56, we need to find the multiples of 8 and 56 (multiples of 8 = 8, 16, 24, 32 . . . . 56; multiples of 56 = 56, 112, 168, 224) and choose the smallest multiple that is exactly divisible by 8 and 56, i.e., 56.

What are the Methods to Find LCM of 8 and 56?

The commonly used methods to find the LCM of 8 and 56 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

Which of the following is the LCM of 8 and 56? 18, 20, 56, 35

The value of LCM of 8, 56 is the smallest common multiple of 8 and 56. The number satisfying the given condition is 56.

How to Find the LCM of 8 and 56 by Prime Factorization?

To find the LCM of 8 and 56 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (56 = 2 × 2 × 2 × 7). LCM of 8 and 56 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 56.
⇒ LCM of 8, 56 = 2³ × 7¹ = 56.

If the LCM of 56 and 8 is 56, Find its GCF.

LCM(56, 8) × GCF(56, 8) = 56 × 8
Since the LCM of 56 and 8 = 56
⇒ 56 × GCF(56, 8) = 448
Therefore, the GCF = 448/56 = 8.