What is the Least Common Multiple of 76320 and 76334?

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 76334 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 76334, than apply into the LCM equation.

GCF(76320,76334) = 2
LCM(76320,76334) = ( 76320 × 76334) / 2
LCM(76320,76334) = 5825810880 / 2
LCM(76320,76334) = 2912905440

Least Common Multiple (LCM) of 76320 and 76334 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76320 and 76334. First we will calculate the prime factors of 76320 and 76334.

Prime Factorization of 76320

Prime Factorization of 76334

Now multiplying the highest exponent prime factors to calculate the LCM of 76320 and 76334.

LCM(76320,76334) = 2⁵ × 3² × 5¹ × 53¹ × 38167¹
LCM(76320,76334) = 2912905440