Least Common Multiple of 57 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 57 and 64 the smallest integer that is 3648 that is divisible by both numbers.

Least Common Multiple (LCM) of 57 and 64 is 3648.

LCM(57,64) = 3648

LCM of 57 and 64

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

LCM of:
and

Least Common Multiple of 57 and 64

LCM of 57 and 64 is 3648

Least common multiple can be found by multiplying the highest exponent prime factors of 57 and 64. First we will calculate the prime factors of 57 and 64.

Prime Factorization of 57


3 57
19 19
1

Prime factors of 57 are 3,19. Prime factorization of 57 in exponential form is:

57 = 31×191

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 57 and 64.

LCM(57,64) = 26×31×191
LCM(57,64) = 3648

Factors of 57

List of positive integer factors of 57 that divides 57 without a remainder.

1, 3, 19, 57

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 57 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 57 and 64, than apply into the LCM equation.

GCF(57,64) = 1
LCM(57,64) = ( 57 × 64) / 1
LCM(57,64) = 3648 / 1
LCM(57,64) = 3648

Properties of LCM 57 and 64

(i) The LCM of 64 and 57 is associative

LCM of 57 and 64 = LCM of 64 and 57

Related Least Common Multiples of 57

Related Least Common Multiples of 64

Frequently Asked Questions on LCM of 57 and 64

1. What is the LCM of 57 and 64?

Answer: LCM of 57 and 64 is 3648.

2. What are the Factors of 57?

Answer: Factors of 57 are 1, 3, 19, 57. There are 4 integers that are factors of 57. The greatest factor of 57 is 57.

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 57 and 64?

Answer:

Least Common Multiple of 57 and 64 = 3648

Step 1: Find the prime factorization of 57

57 = 3 x 19

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 = 3648 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 19

Step 4: Therefore, the least common multiple of 57 and 64 is 3648.