What is the Least Common Multiple of 21504 and 21509?

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 21509 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 21509, than apply into the LCM equation.

GCF(21504,21509) = 1
LCM(21504,21509) = ( 21504 × 21509) / 1
LCM(21504,21509) = 462529536 / 1
LCM(21504,21509) = 462529536

Least Common Multiple (LCM) of 21504 and 21509 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21504 and 21509. First we will calculate the prime factors of 21504 and 21509.

Prime Factorization of 21504

Prime Factorization of 21509

Now multiplying the highest exponent prime factors to calculate the LCM of 21504 and 21509.

LCM(21504,21509) = 2¹⁰ × 3¹ × 7¹ × 137¹ × 157¹
LCM(21504,21509) = 462529536