What is the Least Common Multiple of 31980 and 31996?

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 31996 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 31996, than apply into the LCM equation.

GCF(31980,31996) = 4
LCM(31980,31996) = ( 31980 × 31996) / 4
LCM(31980,31996) = 1023232080 / 4
LCM(31980,31996) = 255808020

Least Common Multiple (LCM) of 31980 and 31996 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31980 and 31996. First we will calculate the prime factors of 31980 and 31996.

Prime Factorization of 31980

Prime Factorization of 31996

Now multiplying the highest exponent prime factors to calculate the LCM of 31980 and 31996.

LCM(31980,31996) = 2² × 3¹ × 5¹ × 13¹ × 41¹ × 19¹ × 421¹
LCM(31980,31996) = 255808020