What is the Least Common Multiple of 31950 and 31968?

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 31950 and 31968 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31950 and 31968, than apply into the LCM equation.

GCF(31950,31968) = 18
LCM(31950,31968) = ( 31950 × 31968) / 18
LCM(31950,31968) = 1021377600 / 18
LCM(31950,31968) = 56743200

Least Common Multiple (LCM) of 31950 and 31968 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31950 and 31968. First we will calculate the prime factors of 31950 and 31968.

Prime Factorization of 31950

Prime Factorization of 31968

Now multiplying the highest exponent prime factors to calculate the LCM of 31950 and 31968.

LCM(31950,31968) = 2⁵ × 3³ × 5² × 71¹ × 37¹
LCM(31950,31968) = 56743200