What is the Least Common Multiple of 12102 and 12117?

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 12102 and 12117 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12102 and 12117, than apply into the LCM equation.

GCF(12102,12117) = 3
LCM(12102,12117) = ( 12102 × 12117) / 3
LCM(12102,12117) = 146639934 / 3
LCM(12102,12117) = 48879978

Least Common Multiple (LCM) of 12102 and 12117 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12102 and 12117. First we will calculate the prime factors of 12102 and 12117.

Prime Factorization of 12102

Prime Factorization of 12117

Now multiplying the highest exponent prime factors to calculate the LCM of 12102 and 12117.

LCM(12102,12117) = 2¹ × 3¹ × 2017¹ × 7¹ × 577¹
LCM(12102,12117) = 48879978