Least Common Multiple of 132 and 138

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 132 and 138 the smallest integer that is 3036 that is divisible by both numbers.

Least Common Multiple (LCM) of 132 and 138 is 3036.

LCM(132,138) = 3036

LCM of 132 and 138

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

LCM of:
and

Least Common Multiple of 132 and 138

LCM of 132 and 138 is 3036

Least common multiple can be found by multiplying the highest exponent prime factors of 132 and 138. First we will calculate the prime factors of 132 and 138.

Prime Factorization of 132


2 132
2 66
3 33
11 11
1

Prime factors of 132 are 2, 3,11. Prime factorization of 132 in exponential form is:

132 = 22×31×111

Prime Factorization of 138


2 138
3 69
23 23
1

Prime factors of 138 are 2, 3,23. Prime factorization of 138 in exponential form is:

138 = 21×31×231

Now multiplying the highest exponent prime factors to calculate the LCM of 132 and 138.

LCM(132,138) = 22×31×111×231
LCM(132,138) = 3036

Factors of 132

List of positive integer factors of 132 that divides 132 without a remainder.

1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132

Factors of 138

List of positive integer factors of 138 that divides 138 without a remainder.

1, 2, 3, 6, 23, 46, 69, 138

Least Common Multiple of 132 and 138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 132 and 138, than apply into the LCM equation.

GCF(132,138) = 6
LCM(132,138) = ( 132 × 138) / 6
LCM(132,138) = 18216 / 6
LCM(132,138) = 3036

Properties of LCM 132 and 138

(i) The LCM of 138 and 132 is associative

LCM of 132 and 138 = LCM of 138 and 132

Related Least Common Multiples of 132

Related Least Common Multiples of 138

Frequently Asked Questions on LCM of 132 and 138

1. What is the LCM of 132 and 138?

Answer: LCM of 132 and 138 is 3036.

2. What are the Factors of 132?

Answer: Factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132. There are 12 integers that are factors of 132. The greatest factor of 132 is 132.

3. What are the Factors of 138?

Answer: Factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138. There are 8 integers that are factors of 138. The greatest factor of 138 is 138.

4. How to Find the LCM of 132 and 138?

Answer:

Least Common Multiple of 132 and 138 = 3036

Step 1: Find the prime factorization of 132

132 = 2 x 2 x 3 x 11

Step 2: Find the prime factorization of 138

138 = 2 x 3 x 23

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

LCM = 3036 = 2 x 2 x 3 x 11 x 23

Step 4: Therefore, the least common multiple of 132 and 138 is 3036.