What is the Least Common Multiple of 109 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 109 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 109 and 117, than apply into the LCM equation.

GCF(109,117) = 1
LCM(109,117) = ( 109 × 117) / 1
LCM(109,117) = 12753 / 1
LCM(109,117) = 12753

Least Common Multiple (LCM) of 109 and 117 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 109 and 117. First we will calculate the prime factors of 109 and 117.

Prime Factorization of 109

Prime Factorization of 117

Now multiplying the highest exponent prime factors to calculate the LCM of 109 and 117.

LCM(109,117) = 109¹ × 3² × 13¹
LCM(109,117) = 12753