Least Common Multiple of 54 and 57

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 57 the smallest integer that is 1026 that is divisible by both numbers.

Least Common Multiple (LCM) of 54 and 57 is 1026.

LCM(54,57) = 1026

LCM of 54 and 57

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

LCM of:
and

Least Common Multiple of 54 and 57

LCM of 54 and 57 is 1026

Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 57. First we will calculate the prime factors of 54 and 57.

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 57


3 57
19 19
1

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

57 = 31×191

Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 57.

LCM(54,57) = 21×33×191
LCM(54,57) = 1026

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 57

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

1, 3, 19, 57

Least Common Multiple of 54 and 57 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 57, than apply into the LCM equation.

GCF(54,57) = 3
LCM(54,57) = ( 54 × 57) / 3
LCM(54,57) = 3078 / 3
LCM(54,57) = 1026

Properties of LCM 54 and 57

(i) The LCM of 57 and 54 is associative

LCM of 54 and 57 = LCM of 57 and 54

Related Least Common Multiples of 54

Related Least Common Multiples of 57

Frequently Asked Questions on LCM of 54 and 57

1. What is the LCM of 54 and 57?

Answer: LCM of 54 and 57 is 1026.

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 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.

4. How to Find the LCM of 54 and 57?

Answer:

Least Common Multiple of 54 and 57 = 1026

Step 1: Find the prime factorization of 54

54 = 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 57

57 = 3 x 19

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

LCM = 1026 = 2 x 3 x 3 x 3 x 19

Step 4: Therefore, the least common multiple of 54 and 57 is 1026.