What is the Least Common Multiple of 31404 and 31416?

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 31404 and 31416 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31404 and 31416, than apply into the LCM equation.

GCF(31404,31416) = 12
LCM(31404,31416) = ( 31404 × 31416) / 12
LCM(31404,31416) = 986588064 / 12
LCM(31404,31416) = 82215672

Least Common Multiple (LCM) of 31404 and 31416 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31404 and 31416. First we will calculate the prime factors of 31404 and 31416.

Prime Factorization of 31404

Prime Factorization of 31416

Now multiplying the highest exponent prime factors to calculate the LCM of 31404 and 31416.

LCM(31404,31416) = 2³ × 3¹ × 2617¹ × 7¹ × 11¹ × 17¹
LCM(31404,31416) = 82215672