What is the Least Common Multiple of 31564 and 31574?

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 31564 and 31574 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31564 and 31574, than apply into the LCM equation.

GCF(31564,31574) = 2
LCM(31564,31574) = ( 31564 × 31574) / 2
LCM(31564,31574) = 996601736 / 2
LCM(31564,31574) = 498300868

Least Common Multiple (LCM) of 31564 and 31574 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31564 and 31574. First we will calculate the prime factors of 31564 and 31574.

Prime Factorization of 31564

Prime Factorization of 31574

Now multiplying the highest exponent prime factors to calculate the LCM of 31564 and 31574.

LCM(31564,31574) = 2² × 13¹ × 607¹ × 15787¹
LCM(31564,31574) = 498300868