Least Common Multiple of 135 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 135 and 138 the smallest integer that is 6210 that is divisible by both numbers.

Least Common Multiple (LCM) of 135 and 138 is 6210.

LCM(135,138) = 6210

LCM of 135 and 138

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

LCM of:
and

Least Common Multiple of 135 and 138

LCM of 135 and 138 is 6210

Least common multiple can be found by multiplying the highest exponent prime factors of 135 and 138. First we will calculate the prime factors of 135 and 138.

Prime Factorization of 135


3 135
3 45
3 15
5 5
1

Prime factors of 135 are 3,5. Prime factorization of 135 in exponential form is:

135 = 33×51

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 135 and 138.

LCM(135,138) = 21×33×51×231
LCM(135,138) = 6210

Factors of 135

List of positive integer factors of 135 that divides 135 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135

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 135 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 135 and 138, than apply into the LCM equation.

GCF(135,138) = 3
LCM(135,138) = ( 135 × 138) / 3
LCM(135,138) = 18630 / 3
LCM(135,138) = 6210

Properties of LCM 135 and 138

(i) The LCM of 138 and 135 is associative

LCM of 135 and 138 = LCM of 138 and 135

Related Least Common Multiples of 135

Related Least Common Multiples of 138

Frequently Asked Questions on LCM of 135 and 138

1. What is the LCM of 135 and 138?

Answer: LCM of 135 and 138 is 6210.

2. What are the Factors of 135?

Answer: Factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135. There are 8 integers that are factors of 135. The greatest factor of 135 is 135.

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 135 and 138?

Answer:

Least Common Multiple of 135 and 138 = 6210

Step 1: Find the prime factorization of 135

135 = 3 x 3 x 3 x 5

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 = 6210 = 2 x 3 x 3 x 3 x 5 x 23

Step 4: Therefore, the least common multiple of 135 and 138 is 6210.