What is the Least Common Multiple of 76320 and 76335?

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 76320 and 76335 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76320 and 76335, than apply into the LCM equation.

GCF(76320,76335) = 15
LCM(76320,76335) = ( 76320 × 76335) / 15
LCM(76320,76335) = 5825887200 / 15
LCM(76320,76335) = 388392480

Least Common Multiple (LCM) of 76320 and 76335 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76320 and 76335. First we will calculate the prime factors of 76320 and 76335.

Prime Factorization of 76320

Prime Factorization of 76335

Now multiplying the highest exponent prime factors to calculate the LCM of 76320 and 76335.

LCM(76320,76335) = 2⁵ × 3² × 5¹ × 53¹ × 7¹ × 727¹
LCM(76320,76335) = 388392480