What is the Least Common Multiple of 31560 and 31578?

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 31560 and 31578 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31560 and 31578, than apply into the LCM equation.

GCF(31560,31578) = 6
LCM(31560,31578) = ( 31560 × 31578) / 6
LCM(31560,31578) = 996601680 / 6
LCM(31560,31578) = 166100280

Least Common Multiple (LCM) of 31560 and 31578 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31560 and 31578. First we will calculate the prime factors of 31560 and 31578.

Prime Factorization of 31560

Prime Factorization of 31578

Now multiplying the highest exponent prime factors to calculate the LCM of 31560 and 31578.

LCM(31560,31578) = 2³ × 3¹ × 5¹ × 263¹ × 19¹ × 277¹
LCM(31560,31578) = 166100280