# What is the Least Common Multiple of 138 and 152?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 138 and 152 is 10488.

LCM(138,152) = 10488

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## Least Common Multiple of 138 and 152 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 138 and 152, than apply into the LCM equation.

GCF(138,152) = 2
LCM(138,152) = ( 138 × 152) / 2
LCM(138,152) = 20976 / 2
LCM(138,152) = 10488

## Least Common Multiple (LCM) of 138 and 152 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 138 and 152. First we will calculate the prime factors of 138 and 152.

### Prime Factorization of 138

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

138 = 21 × 31 × 231

### Prime Factorization of 152

Prime factors of 152 are 2, 19. Prime factorization of 152 in exponential form is:

152 = 23 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 138 and 152.

LCM(138,152) = 23 × 31 × 231 × 191
LCM(138,152) = 10488