Least Common Multiple of 136 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 136 and 138 the smallest integer that is 9384 that is divisible by both numbers.

Least Common Multiple (LCM) of 136 and 138 is 9384.

LCM(136,138) = 9384

LCM of 136 and 138

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

LCM of:
and

Least Common Multiple of 136 and 138

LCM of 136 and 138 is 9384

Least common multiple can be found by multiplying the highest exponent prime factors of 136 and 138. First we will calculate the prime factors of 136 and 138.

Prime Factorization of 136


2 136
2 68
2 34
17 17
1

Prime factors of 136 are 2,17. Prime factorization of 136 in exponential form is:

136 = 23×171

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 136 and 138.

LCM(136,138) = 23×31×171×231
LCM(136,138) = 9384

Factors of 136

List of positive integer factors of 136 that divides 136 without a remainder.

1, 2, 4, 8, 17, 34, 68, 136

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 136 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 136 and 138, than apply into the LCM equation.

GCF(136,138) = 2
LCM(136,138) = ( 136 × 138) / 2
LCM(136,138) = 18768 / 2
LCM(136,138) = 9384

Properties of LCM 136 and 138

(i) The LCM of 138 and 136 is associative

LCM of 136 and 138 = LCM of 138 and 136

Related Least Common Multiples of 136

Related Least Common Multiples of 138

Frequently Asked Questions on LCM of 136 and 138

1. What is the LCM of 136 and 138?

Answer: LCM of 136 and 138 is 9384.

2. What are the Factors of 136?

Answer: Factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136. There are 8 integers that are factors of 136. The greatest factor of 136 is 136.

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 136 and 138?

Answer:

Least Common Multiple of 136 and 138 = 9384

Step 1: Find the prime factorization of 136

136 = 2 x 2 x 2 x 17

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 = 9384 = 2 x 2 x 2 x 3 x 17 x 23

Step 4: Therefore, the least common multiple of 136 and 138 is 9384.