What is the Least Common Multiple of 76314 and 76320?

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 76314 and 76320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76314 and 76320, than apply into the LCM equation.

GCF(76314,76320) = 6
LCM(76314,76320) = ( 76314 × 76320) / 6
LCM(76314,76320) = 5824284480 / 6
LCM(76314,76320) = 970714080

Least Common Multiple (LCM) of 76314 and 76320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76314 and 76320. First we will calculate the prime factors of 76314 and 76320.

Prime Factorization of 76314

Prime Factorization of 76320

Now multiplying the highest exponent prime factors to calculate the LCM of 76314 and 76320.

LCM(76314,76320) = 2⁵ × 3² × 7¹ × 23¹ × 79¹ × 5¹ × 53¹
LCM(76314,76320) = 970714080