Least Common Multiple of 54 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 54 and 64 the smallest integer that is 1728 that is divisible by both numbers.

Least Common Multiple (LCM) of 54 and 64 is 1728.

LCM(54,64) = 1728

LCM of 54 and 64

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

LCM of:
and

Least Common Multiple of 54 and 64

LCM of 54 and 64 is 1728

Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 64. First we will calculate the prime factors of 54 and 64.

Prime Factorization of 54


2 54
3 27
3 9
3 3
1

Prime factors of 54 are 2,3. Prime factorization of 54 in exponential form is:

54 = 21×33

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 54 and 64.

LCM(54,64) = 26×33
LCM(54,64) = 1728

Factors of 54

List of positive integer factors of 54 that divides 54 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54

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 54 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 54 and 64, than apply into the LCM equation.

GCF(54,64) = 2
LCM(54,64) = ( 54 × 64) / 2
LCM(54,64) = 3456 / 2
LCM(54,64) = 1728

Properties of LCM 54 and 64

(i) The LCM of 64 and 54 is associative

LCM of 54 and 64 = LCM of 64 and 54

Related Least Common Multiples of 54

Related Least Common Multiples of 64

Frequently Asked Questions on LCM of 54 and 64

1. What is the LCM of 54 and 64?

Answer: LCM of 54 and 64 is 1728.

2. What are the Factors of 54?

Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.

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 54 and 64?

Answer:

Least Common Multiple of 54 and 64 = 1728

Step 1: Find the prime factorization of 54

54 = 2 x 3 x 3 x 3

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 = 1728 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

Step 4: Therefore, the least common multiple of 54 and 64 is 1728.