What is the Least Common Multiple of 31954 and 31972?

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 31954 and 31972 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31954 and 31972, than apply into the LCM equation.

GCF(31954,31972) = 2
LCM(31954,31972) = ( 31954 × 31972) / 2
LCM(31954,31972) = 1021633288 / 2
LCM(31954,31972) = 510816644

Least Common Multiple (LCM) of 31954 and 31972 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31954 and 31972. First we will calculate the prime factors of 31954 and 31972.

Prime Factorization of 31954

Prime Factorization of 31972

Now multiplying the highest exponent prime factors to calculate the LCM of 31954 and 31972.

LCM(31954,31972) = 2² × 13¹ × 1229¹ × 7993¹
LCM(31954,31972) = 510816644