What is the Least Common Multiple of 21504 and 21524?

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 21504 and 21524 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21504 and 21524, than apply into the LCM equation.

GCF(21504,21524) = 4
LCM(21504,21524) = ( 21504 × 21524) / 4
LCM(21504,21524) = 462852096 / 4
LCM(21504,21524) = 115713024

Least Common Multiple (LCM) of 21504 and 21524 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21504 and 21524. First we will calculate the prime factors of 21504 and 21524.

Prime Factorization of 21504

Prime Factorization of 21524

Now multiplying the highest exponent prime factors to calculate the LCM of 21504 and 21524.

LCM(21504,21524) = 2¹⁰ × 3¹ × 7¹ × 5381¹
LCM(21504,21524) = 115713024