What is the Least Common Multiple of 86304 and 86310?

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 86304 and 86310 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 86304 and 86310, than apply into the LCM equation.

GCF(86304,86310) = 6
LCM(86304,86310) = ( 86304 × 86310) / 6
LCM(86304,86310) = 7448898240 / 6
LCM(86304,86310) = 1241483040

Least Common Multiple (LCM) of 86304 and 86310 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 86304 and 86310. First we will calculate the prime factors of 86304 and 86310.

Prime Factorization of 86304

Prime Factorization of 86310

Now multiplying the highest exponent prime factors to calculate the LCM of 86304 and 86310.

LCM(86304,86310) = 2⁵ × 3² × 29¹ × 31¹ × 5¹ × 7¹ × 137¹
LCM(86304,86310) = 1241483040