What is the Least Common Multiple of 31980 and 31992?

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 31980 and 31992 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31980 and 31992, than apply into the LCM equation.

GCF(31980,31992) = 12
LCM(31980,31992) = ( 31980 × 31992) / 12
LCM(31980,31992) = 1023104160 / 12
LCM(31980,31992) = 85258680

Least Common Multiple (LCM) of 31980 and 31992 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31980 and 31992. First we will calculate the prime factors of 31980 and 31992.

Prime Factorization of 31980

Prime Factorization of 31992

Now multiplying the highest exponent prime factors to calculate the LCM of 31980 and 31992.

LCM(31980,31992) = 2³ × 3¹ × 5¹ × 13¹ × 41¹ × 31¹ × 43¹
LCM(31980,31992) = 85258680