LCM of 64 and 72

LCM of 64 and 72 is the smallest number among all common multiples of 64 and 72. The first few multiples of 64 and 72 are (64, 128, 192, 256, . . . ) and (72, 144, 216, 288, 360, . . . ) respectively. There are 3 commonly used methods to find LCM of 64 and 72 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 64 and 72 is 576.

Explanation:

The LCM of two non-zero integers, x(64) and y(72), is the smallest positive integer m(576) that is divisible by both x(64) and y(72) without any remainder.

Let's look at the different methods for finding the LCM of 64 and 72.

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

LCM of 64 and 72 by Listing Multiples

To calculate the LCM of 64 and 72 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, . . . ) and 72 (72, 144, 216, 288, 360, . . . . )
• Step 2: The common multiples from the multiples of 64 and 72 are 576, 1152, . . .
• Step 3: The smallest common multiple of 64 and 72 is 576.

∴ The least common multiple of 64 and 72 = 576.

LCM of 64 and 72 by Division Method

To calculate the LCM of 64 and 72 by the division method, we will divide the numbers(64, 72) by their prime factors (preferably common). The product of these divisors gives the LCM of 64 and 72.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 64 and 72. Write this prime number(2) on the left of the given numbers(64 and 72), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (64, 72) 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 72 is the product of all prime numbers on the left, i.e. LCM(64, 72) by division method = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 = 576.

LCM of 64 and 72 by Prime Factorization

Prime factorization of 64 and 72 is (2 × 2 × 2 × 2 × 2 × 2) = 2⁶ and (2 × 2 × 2 × 3 × 3) = 2³ × 3² respectively. LCM of 64 and 72 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁶ × 3² = 576.
Hence, the LCM of 64 and 72 by prime factorization is 576.

☛ Also Check:

• LCM of 75 and 100 - 300
• LCM of 3, 4, 5 and 6 - 60
• LCM of 4 and 14 - 28
• LCM of 3, 4 and 9 - 36
• LCM of 17 and 34 - 34
• LCM of 16 and 64 - 64
• LCM of 16 and 60 - 240

FAQs on LCM of 64 and 72

What is the LCM of 64 and 72?

The LCM of 64 and 72 is 576. To find the LCM of 64 and 72, we need to find the multiples of 64 and 72 (multiples of 64 = 64, 128, 192, 256 . . . . 576; multiples of 72 = 72, 144, 216, 288 . . . . 576) and choose the smallest multiple that is exactly divisible by 64 and 72, i.e., 576.

If the LCM of 72 and 64 is 576, Find its GCF.

LCM(72, 64) × GCF(72, 64) = 72 × 64
Since the LCM of 72 and 64 = 576
⇒ 576 × GCF(72, 64) = 4608
Therefore, the greatest common factor = 4608/576 = 8.

What is the Relation Between GCF and LCM of 64, 72?

The following equation can be used to express the relation between GCF and LCM of 64 and 72, i.e. GCF × LCM = 64 × 72.

What is the Least Perfect Square Divisible by 64 and 72?

The least number divisible by 64 and 72 = LCM(64, 72)
LCM of 64 and 72 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 64 and 72 = 576 [Square root of 576 = √576 = ±24]
Therefore, 576 is the required number.

How to Find the LCM of 64 and 72 by Prime Factorization?

To find the LCM of 64 and 72 using prime factorization, we will find the prime factors, (64 = 2 × 2 × 2 × 2 × 2 × 2) and (72 = 2 × 2 × 2 × 3 × 3). LCM of 64 and 72 is the product of prime factors raised to their respective highest exponent among the numbers 64 and 72.
⇒ LCM of 64, 72 = 2⁶ × 3² = 576.