What is the Least Common Multiple of 31146 and 31164?

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 31146 and 31164 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31146 and 31164, than apply into the LCM equation.

GCF(31146,31164) = 6
LCM(31146,31164) = ( 31146 × 31164) / 6
LCM(31146,31164) = 970633944 / 6
LCM(31146,31164) = 161772324

Least Common Multiple (LCM) of 31146 and 31164 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31146 and 31164. First we will calculate the prime factors of 31146 and 31164.

Prime Factorization of 31146

Prime Factorization of 31164

Now multiplying the highest exponent prime factors to calculate the LCM of 31146 and 31164.

LCM(31146,31164) = 2² × 3¹ × 29¹ × 179¹ × 7² × 53¹
LCM(31146,31164) = 161772324