Least Common Multiple of 60 and 64

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 60 and 64 the smallest integer that is 960 that is divisible by both numbers.

Least Common Multiple (LCM) of 60 and 64 is 960.

LCM(60,64) = 960

LCM of 60 and 64

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

LCM of:
and

Least Common Multiple of 60 and 64

LCM of 60 and 64 is 960

Least common multiple can be found by multiplying the highest exponent prime factors of 60 and 64. First we will calculate the prime factors of 60 and 64.

Prime Factorization of 60


2 60
2 30
3 15
5 5
1

Prime factors of 60 are 2, 3,5. Prime factorization of 60 in exponential form is:

60 = 22×31×51

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

Now multiplying the highest exponent prime factors to calculate the LCM of 60 and 64.

LCM(60,64) = 26×31×51
LCM(60,64) = 960

Factors of 60

List of positive integer factors of 60 that divides 60 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Factors of 64

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

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

Least Common Multiple of 60 and 64 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 60 and 64, than apply into the LCM equation.

GCF(60,64) = 4
LCM(60,64) = ( 60 × 64) / 4
LCM(60,64) = 3840 / 4
LCM(60,64) = 960

Properties of LCM 60 and 64

(i) The LCM of 64 and 60 is associative

LCM of 60 and 64 = LCM of 64 and 60

Related Least Common Multiples of 60

Related Least Common Multiples of 64

Frequently Asked Questions on LCM of 60 and 64

1. What is the LCM of 60 and 64?

Answer: LCM of 60 and 64 is 960.

2. What are the Factors of 60?

Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.

3. 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.

4. How to Find the LCM of 60 and 64?

Answer:

Least Common Multiple of 60 and 64 = 960

Step 1: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 64

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

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

LCM = 960 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 60 and 64 is 960.