Least Common Multiple of 54 and 66

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 66 the smallest integer that is 594 that is divisible by both numbers.

Least Common Multiple (LCM) of 54 and 66 is 594.

LCM(54,66) = 594

LCM of 54 and 66

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

LCM of:
and

Least Common Multiple of 54 and 66

LCM of 54 and 66 is 594

Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 66. First we will calculate the prime factors of 54 and 66.

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 66


2 66
3 33
11 11
1

Prime factors of 66 are 2, 3,11. Prime factorization of 66 in exponential form is:

66 = 21×31×111

Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 66.

LCM(54,66) = 21×33×111
LCM(54,66) = 594

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 66

List of positive integer factors of 66 that divides 66 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66

Least Common Multiple of 54 and 66 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 66, than apply into the LCM equation.

GCF(54,66) = 6
LCM(54,66) = ( 54 × 66) / 6
LCM(54,66) = 3564 / 6
LCM(54,66) = 594

Properties of LCM 54 and 66

(i) The LCM of 66 and 54 is associative

LCM of 54 and 66 = LCM of 66 and 54

Related Least Common Multiples of 54

Related Least Common Multiples of 66

Frequently Asked Questions on LCM of 54 and 66

1. What is the LCM of 54 and 66?

Answer: LCM of 54 and 66 is 594.

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 66?

Answer: Factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66. There are 8 integers that are factors of 66. The greatest factor of 66 is 66.

4. How to Find the LCM of 54 and 66?

Answer:

Least Common Multiple of 54 and 66 = 594

Step 1: Find the prime factorization of 54

54 = 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 66

66 = 2 x 3 x 11

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

LCM = 594 = 2 x 3 x 3 x 3 x 11

Step 4: Therefore, the least common multiple of 54 and 66 is 594.