What is the Least Common Multiple of 31971 and 31989?

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 31971 and 31989 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31971 and 31989, than apply into the LCM equation.

GCF(31971,31989) = 3
LCM(31971,31989) = ( 31971 × 31989) / 3
LCM(31971,31989) = 1022720319 / 3
LCM(31971,31989) = 340906773

Least Common Multiple (LCM) of 31971 and 31989 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31971 and 31989. First we will calculate the prime factors of 31971 and 31989.

Prime Factorization of 31971

Prime Factorization of 31989

Now multiplying the highest exponent prime factors to calculate the LCM of 31971 and 31989.

LCM(31971,31989) = 3¹ × 10657¹ × 10663¹
LCM(31971,31989) = 340906773