What is the Least Common Multiple of 78312 and 78324?

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 78312 and 78324 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78312 and 78324, than apply into the LCM equation.

GCF(78312,78324) = 12
LCM(78312,78324) = ( 78312 × 78324) / 12
LCM(78312,78324) = 6133709088 / 12
LCM(78312,78324) = 511142424

Least Common Multiple (LCM) of 78312 and 78324 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78312 and 78324. First we will calculate the prime factors of 78312 and 78324.

Prime Factorization of 78312

Prime Factorization of 78324

Now multiplying the highest exponent prime factors to calculate the LCM of 78312 and 78324.

LCM(78312,78324) = 2³ × 3¹ × 13¹ × 251¹ × 61¹ × 107¹
LCM(78312,78324) = 511142424