What is the Least Common Multiple of 31980 and 31986?

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 31986 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 31986, than apply into the LCM equation.

GCF(31980,31986) = 6
LCM(31980,31986) = ( 31980 × 31986) / 6
LCM(31980,31986) = 1022912280 / 6
LCM(31980,31986) = 170485380

Least Common Multiple (LCM) of 31980 and 31986 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31980 and 31986. First we will calculate the prime factors of 31980 and 31986.

Prime Factorization of 31980

Prime Factorization of 31986

Now multiplying the highest exponent prime factors to calculate the LCM of 31980 and 31986.

LCM(31980,31986) = 2² × 3² × 5¹ × 13¹ × 41¹ × 1777¹
LCM(31980,31986) = 170485380