Least Common Multiple of 54 and 60

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 60 the smallest integer that is 540 that is divisible by both numbers.

Least Common Multiple (LCM) of 54 and 60 is 540.

LCM(54,60) = 540

LCM of 54 and 60

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

LCM of:
and

Least Common Multiple of 54 and 60

LCM of 54 and 60 is 540

Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 60. First we will calculate the prime factors of 54 and 60.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 60.

LCM(54,60) = 22×33×51
LCM(54,60) = 540

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 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

Least Common Multiple of 54 and 60 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 60, than apply into the LCM equation.

GCF(54,60) = 6
LCM(54,60) = ( 54 × 60) / 6
LCM(54,60) = 3240 / 6
LCM(54,60) = 540

Properties of LCM 54 and 60

(i) The LCM of 60 and 54 is associative

LCM of 54 and 60 = LCM of 60 and 54

Related Least Common Multiples of 54

Related Least Common Multiples of 60

Frequently Asked Questions on LCM of 54 and 60

1. What is the LCM of 54 and 60?

Answer: LCM of 54 and 60 is 540.

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 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.

4. How to Find the LCM of 54 and 60?

Answer:

Least Common Multiple of 54 and 60 = 540

Step 1: Find the prime factorization of 54

54 = 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

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

LCM = 540 = 2 x 2 x 3 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 54 and 60 is 540.