What is the Least Common Multiple of 13715 and 13728?

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 13715 and 13728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13715 and 13728, than apply into the LCM equation.

GCF(13715,13728) = 13
LCM(13715,13728) = ( 13715 × 13728) / 13
LCM(13715,13728) = 188279520 / 13
LCM(13715,13728) = 14483040

Least Common Multiple (LCM) of 13715 and 13728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13715 and 13728. First we will calculate the prime factors of 13715 and 13728.

Prime Factorization of 13715

Prime Factorization of 13728

Now multiplying the highest exponent prime factors to calculate the LCM of 13715 and 13728.

LCM(13715,13728) = 5¹ × 13¹ × 211¹ × 2⁵ × 3¹ × 11¹
LCM(13715,13728) = 14483040