What is the Least Common Multiple of 138 and 150?

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 of 138 and 150 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 150, than apply into the LCM equation.

GCF(138,150) = 6
LCM(138,150) = ( 138 × 150) / 6
LCM(138,150) = 20700 / 6
LCM(138,150) = 3450

Least Common Multiple (LCM) of 138 and 150 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 138 and 150. First we will calculate the prime factors of 138 and 150.

Prime Factorization of 138

Prime Factorization of 150

Now multiplying the highest exponent prime factors to calculate the LCM of 138 and 150.

LCM(138,150) = 2¹ × 3¹ × 23¹ × 5²
LCM(138,150) = 3450