LCM of 64 and 96

LCM of 64 and 96 is the smallest number among all common multiples of 64 and 96. The first few multiples of 64 and 96 are (64, 128, 192, 256, 320, . . . ) and (96, 192, 288, 384, 480, . . . ) respectively. There are 3 commonly used methods to find LCM of 64 and 96 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 64 and 96 is 192.

Explanation:

The LCM of two non-zero integers, x(64) and y(96), is the smallest positive integer m(192) that is divisible by both x(64) and y(96) without any remainder.

The methods to find the LCM of 64 and 96 are explained below.

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

LCM of 64 and 96 by Division Method

To calculate the LCM of 64 and 96 by the division method, we will divide the numbers(64, 96) by their prime factors (preferably common). The product of these divisors gives the LCM of 64 and 96.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 64 and 96. Write this prime number(2) on the left of the given numbers(64 and 96), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (64, 96) 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 64 and 96 is the product of all prime numbers on the left, i.e. LCM(64, 96) by division method = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 192.

LCM of 64 and 96 by Listing Multiples

To calculate the LCM of 64 and 96 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 64 (64, 128, 192, 256, 320, . . . ) and 96 (96, 192, 288, 384, 480, . . . . )
• Step 2: The common multiples from the multiples of 64 and 96 are 192, 384, . . .
• Step 3: The smallest common multiple of 64 and 96 is 192.

∴ The least common multiple of 64 and 96 = 192.

LCM of 64 and 96 by Prime Factorization

Prime factorization of 64 and 96 is (2 × 2 × 2 × 2 × 2 × 2) = 2⁶ and (2 × 2 × 2 × 2 × 2 × 3) = 2⁵ × 3¹ respectively. LCM of 64 and 96 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁶ × 3¹ = 192.
Hence, the LCM of 64 and 96 by prime factorization is 192.

☛ Also Check:

• LCM of 8 and 20 - 40
• LCM of 20, 30 and 60 - 60
• LCM of 5 and 25 - 25
• LCM of 18 and 63 - 126
• LCM of 12, 15 and 18 - 180
• LCM of 45 and 50 - 450
• LCM of 3 and 12 - 12

FAQs on LCM of 64 and 96

What is the LCM of 64 and 96?

The LCM of 64 and 96 is 192. To find the least common multiple (LCM) of 64 and 96, we need to find the multiples of 64 and 96 (multiples of 64 = 64, 128, 192, 256; multiples of 96 = 96, 192, 288, 384) and choose the smallest multiple that is exactly divisible by 64 and 96, i.e., 192.

What are the Methods to Find LCM of 64 and 96?

The commonly used methods to find the LCM of 64 and 96 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

How to Find the LCM of 64 and 96 by Prime Factorization?

To find the LCM of 64 and 96 using prime factorization, we will find the prime factors, (64 = 2 × 2 × 2 × 2 × 2 × 2) and (96 = 2 × 2 × 2 × 2 × 2 × 3). LCM of 64 and 96 is the product of prime factors raised to their respective highest exponent among the numbers 64 and 96.
⇒ LCM of 64, 96 = 2⁶ × 3¹ = 192.

What is the Relation Between GCF and LCM of 64, 96?

The following equation can be used to express the relation between GCF and LCM of 64 and 96, i.e. GCF × LCM = 64 × 96.

If the LCM of 96 and 64 is 192, Find its GCF.

LCM(96, 64) × GCF(96, 64) = 96 × 64
Since the LCM of 96 and 64 = 192
⇒ 192 × GCF(96, 64) = 6144
Therefore, the greatest common factor (GCF) = 6144/192 = 32.