What is the Least Common Multiple of 34704 and 34720?

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 34704 and 34720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34704 and 34720, than apply into the LCM equation.

GCF(34704,34720) = 16
LCM(34704,34720) = ( 34704 × 34720) / 16
LCM(34704,34720) = 1204922880 / 16
LCM(34704,34720) = 75307680

Least Common Multiple (LCM) of 34704 and 34720 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34704 and 34720. First we will calculate the prime factors of 34704 and 34720.

Prime Factorization of 34704

Prime Factorization of 34720

Now multiplying the highest exponent prime factors to calculate the LCM of 34704 and 34720.

LCM(34704,34720) = 2⁵ × 3² × 241¹ × 5¹ × 7¹ × 31¹
LCM(34704,34720) = 75307680