What is the Least Common Multiple of 13504 and 13524?

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 13504 and 13524 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13504 and 13524, than apply into the LCM equation.

GCF(13504,13524) = 4
LCM(13504,13524) = ( 13504 × 13524) / 4
LCM(13504,13524) = 182628096 / 4
LCM(13504,13524) = 45657024

Least Common Multiple (LCM) of 13504 and 13524 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13504 and 13524. First we will calculate the prime factors of 13504 and 13524.

Prime Factorization of 13504

Prime Factorization of 13524

Now multiplying the highest exponent prime factors to calculate the LCM of 13504 and 13524.

LCM(13504,13524) = 2⁶ × 211¹ × 3¹ × 7² × 23¹
LCM(13504,13524) = 45657024