What is the Least Common Multiple of 102 and 117?

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 102 and 117 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 102 and 117, than apply into the LCM equation.

GCF(102,117) = 3
LCM(102,117) = ( 102 × 117) / 3
LCM(102,117) = 11934 / 3
LCM(102,117) = 3978

Least Common Multiple (LCM) of 102 and 117 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 102 and 117. First we will calculate the prime factors of 102 and 117.

Prime Factorization of 102

Prime Factorization of 117

Now multiplying the highest exponent prime factors to calculate the LCM of 102 and 117.

LCM(102,117) = 2¹ × 3² × 17¹ × 13¹
LCM(102,117) = 3978