What is the Least Common Multiple of 31944 and 31959?

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 31944 and 31959 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31944 and 31959, than apply into the LCM equation.

GCF(31944,31959) = 3
LCM(31944,31959) = ( 31944 × 31959) / 3
LCM(31944,31959) = 1020898296 / 3
LCM(31944,31959) = 340299432

Least Common Multiple (LCM) of 31944 and 31959 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31944 and 31959. First we will calculate the prime factors of 31944 and 31959.

Prime Factorization of 31944

Prime Factorization of 31959

Now multiplying the highest exponent prime factors to calculate the LCM of 31944 and 31959.

LCM(31944,31959) = 2³ × 3² × 11³ × 53¹ × 67¹
LCM(31944,31959) = 340299432