LCM of 56 and 64

LCM of 56 and 64 is the smallest number among all common multiples of 56 and 64. The first few multiples of 56 and 64 are (56, 112, 168, 224, 280, . . . ) and (64, 128, 192, 256, 320, 384, 448, . . . ) respectively. There are 3 commonly used methods to find LCM of 56 and 64 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 56 and 64 is 448.

Explanation:

The LCM of two non-zero integers, x(56) and y(64), is the smallest positive integer m(448) that is divisible by both x(56) and y(64) without any remainder.

The methods to find the LCM of 56 and 64 are explained below.

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

LCM of 56 and 64 by Prime Factorization

Prime factorization of 56 and 64 is (2 × 2 × 2 × 7) = 2³ × 7¹ and (2 × 2 × 2 × 2 × 2 × 2) = 2⁶ respectively. LCM of 56 and 64 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁶ × 7¹ = 448.
Hence, the LCM of 56 and 64 by prime factorization is 448.

LCM of 56 and 64 by Division Method

To calculate the LCM of 56 and 64 by the division method, we will divide the numbers(56, 64) by their prime factors (preferably common). The product of these divisors gives the LCM of 56 and 64.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 56 and 64. Write this prime number(2) on the left of the given numbers(56 and 64), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (56, 64) 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 56 and 64 is the product of all prime numbers on the left, i.e. LCM(56, 64) by division method = 2 × 2 × 2 × 2 × 2 × 2 × 7 = 448.

LCM of 56 and 64 by Listing Multiples

To calculate the LCM of 56 and 64 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 56 (56, 112, 168, 224, 280, . . . ) and 64 (64, 128, 192, 256, 320, 384, 448, . . . . )
• Step 2: The common multiples from the multiples of 56 and 64 are 448, 896, . . .
• Step 3: The smallest common multiple of 56 and 64 is 448.

∴ The least common multiple of 56 and 64 = 448.

☛ Also Check:

• LCM of 56 and 84 - 168
• LCM of 6, 72 and 120 - 360
• LCM of 45, 60 and 75 - 900
• LCM of 3, 4 and 8 - 24
• LCM of 14 and 28 - 28
• LCM of 2, 4, 6, 8, 10 and 12 - 120
• LCM of 10 and 35 - 70

FAQs on LCM of 56 and 64

What is the LCM of 56 and 64?

The LCM of 56 and 64 is 448. To find the LCM of 56 and 64, we need to find the multiples of 56 and 64 (multiples of 56 = 56, 112, 168, 224 . . . . 448; multiples of 64 = 64, 128, 192, 256 . . . . 448) and choose the smallest multiple that is exactly divisible by 56 and 64, i.e., 448.

How to Find the LCM of 56 and 64 by Prime Factorization?

To find the LCM of 56 and 64 using prime factorization, we will find the prime factors, (56 = 2 × 2 × 2 × 7) and (64 = 2 × 2 × 2 × 2 × 2 × 2). LCM of 56 and 64 is the product of prime factors raised to their respective highest exponent among the numbers 56 and 64.
⇒ LCM of 56, 64 = 2⁶ × 7¹ = 448.

Which of the following is the LCM of 56 and 64? 40, 50, 448, 20

The value of LCM of 56, 64 is the smallest common multiple of 56 and 64. The number satisfying the given condition is 448.

If the LCM of 64 and 56 is 448, Find its GCF.

LCM(64, 56) × GCF(64, 56) = 64 × 56
Since the LCM of 64 and 56 = 448
⇒ 448 × GCF(64, 56) = 3584
Therefore, the greatest common factor = 3584/448 = 8.

What are the Methods to Find LCM of 56 and 64?

The commonly used methods to find the LCM of 56 and 64 are:

• Listing Multiples
• Prime Factorization Method
• Division Method