Least Common Multiple of 64 and 72

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 64 and 72 the smallest integer that is 576 that is divisible by both numbers.

Least Common Multiple (LCM) of 64 and 72 is 576.

LCM(64,72) = 576

LCM of 64 and 72

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 64 and 72

LCM of 64 and 72 is 576

Least common multiple can be found by multiplying the highest exponent prime factors of 64 and 72. First we will calculate the prime factors of 64 and 72.

Prime Factorization of 64


2 64
2 32
2 16
2 8
2 4
2 2
1

Prime factors of 64 are 2. Prime factorization of 64 in exponential form is:

64 = 26

Prime Factorization of 72


2 72
2 36
2 18
3 9
3 3
1

Prime factors of 72 are 2,3. Prime factorization of 72 in exponential form is:

72 = 23×32

Now multiplying the highest exponent prime factors to calculate the LCM of 64 and 72.

LCM(64,72) = 26×32
LCM(64,72) = 576

Factors of 64

List of positive integer factors of 64 that divides 64 without a remainder.

1, 2, 4, 8, 16, 32, 64

Factors of 72

List of positive integer factors of 72 that divides 72 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Least Common Multiple of 64 and 72 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 64 and 72, than apply into the LCM equation.

GCF(64,72) = 8
LCM(64,72) = ( 64 × 72) / 8
LCM(64,72) = 4608 / 8
LCM(64,72) = 576

Properties of LCM 64 and 72

(i) The LCM of 72 and 64 is associative

LCM of 64 and 72 = LCM of 72 and 64

Related Least Common Multiples of 64

Related Least Common Multiples of 72

Frequently Asked Questions on LCM of 64 and 72

1. What is the LCM of 64 and 72?

Answer: LCM of 64 and 72 is 576.

2. What are the Factors of 64?

Answer: Factors of 64 are 1, 2, 4, 8, 16, 32, 64. There are 7 integers that are factors of 64. The greatest factor of 64 is 64.

3. What are the Factors of 72?

Answer: Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. There are 12 integers that are factors of 72. The greatest factor of 72 is 72.

4. How to Find the LCM of 64 and 72?

Answer:

Least Common Multiple of 64 and 72 = 576

Step 1: Find the prime factorization of 64

64 = 2 x 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 72

72 = 2 x 2 x 2 x 3 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 576 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3

Step 4: Therefore, the least common multiple of 64 and 72 is 576.