What is the Least Common Multiple of 31965 and 31980?

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 31965 and 31980 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31965 and 31980, than apply into the LCM equation.

GCF(31965,31980) = 15
LCM(31965,31980) = ( 31965 × 31980) / 15
LCM(31965,31980) = 1022240700 / 15
LCM(31965,31980) = 68149380

Least Common Multiple (LCM) of 31965 and 31980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31965 and 31980. First we will calculate the prime factors of 31965 and 31980.

Prime Factorization of 31965

Prime Factorization of 31980

Now multiplying the highest exponent prime factors to calculate the LCM of 31965 and 31980.

LCM(31965,31980) = 3¹ × 5¹ × 2131¹ × 2² × 13¹ × 41¹
LCM(31965,31980) = 68149380