Least Common Multiple of 137 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 137 and 138 the smallest integer that is 18906 that is divisible by both numbers.

Least Common Multiple (LCM) of 137 and 138 is 18906.

LCM(137,138) = 18906

LCM of 137 and 138

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

LCM of:
and

Least Common Multiple of 137 and 138

LCM of 137 and 138 is 18906

Least common multiple can be found by multiplying the highest exponent prime factors of 137 and 138. First we will calculate the prime factors of 137 and 138.

Prime Factorization of 137


137 137
1

Prime factors of 137 are 137. Prime factorization of 137 in exponential form is:

137 = 1371

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 137 and 138.

LCM(137,138) = 21×31×231×1371
LCM(137,138) = 18906

Factors of 137

List of positive integer factors of 137 that divides 137 without a remainder.

1, 137

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 137 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 137 and 138, than apply into the LCM equation.

GCF(137,138) = 1
LCM(137,138) = ( 137 × 138) / 1
LCM(137,138) = 18906 / 1
LCM(137,138) = 18906

Properties of LCM 137 and 138

(i) The LCM of 138 and 137 is associative

LCM of 137 and 138 = LCM of 138 and 137

Related Least Common Multiples of 137

Related Least Common Multiples of 138

Frequently Asked Questions on LCM of 137 and 138

1. What is the LCM of 137 and 138?

Answer: LCM of 137 and 138 is 18906.

2. What are the Factors of 137?

Answer: Factors of 137 are 1, 137. There are 2 integers that are factors of 137. The greatest factor of 137 is 137.

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 137 and 138?

Answer:

Least Common Multiple of 137 and 138 = 18906

Step 1: Find the prime factorization of 137

137 = 137

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 = 18906 = 2 x 3 x 23 x 137

Step 4: Therefore, the least common multiple of 137 and 138 is 18906.