What is the Least Common Multiple of 15123 and 15138?

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 15123 and 15138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15123 and 15138, than apply into the LCM equation.

GCF(15123,15138) = 3
LCM(15123,15138) = ( 15123 × 15138) / 3
LCM(15123,15138) = 228931974 / 3
LCM(15123,15138) = 76310658

Least Common Multiple (LCM) of 15123 and 15138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15123 and 15138. First we will calculate the prime factors of 15123 and 15138.

Prime Factorization of 15123

Prime Factorization of 15138

Now multiplying the highest exponent prime factors to calculate the LCM of 15123 and 15138.

LCM(15123,15138) = 3² × 71² × 2¹ × 29²
LCM(15123,15138) = 76310658