What is the Least Common Multiple of 13728 and 13746?

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 13728 and 13746 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13728 and 13746, than apply into the LCM equation.

GCF(13728,13746) = 6
LCM(13728,13746) = ( 13728 × 13746) / 6
LCM(13728,13746) = 188705088 / 6
LCM(13728,13746) = 31450848

Least Common Multiple (LCM) of 13728 and 13746 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13728 and 13746. First we will calculate the prime factors of 13728 and 13746.

Prime Factorization of 13728

Prime Factorization of 13746

Now multiplying the highest exponent prime factors to calculate the LCM of 13728 and 13746.

LCM(13728,13746) = 2⁵ × 3¹ × 11¹ × 13¹ × 29¹ × 79¹
LCM(13728,13746) = 31450848