What is the Least Common Multiple of 504 and 521?

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 504 and 521 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 504 and 521, than apply into the LCM equation.

GCF(504,521) = 1
LCM(504,521) = ( 504 × 521) / 1
LCM(504,521) = 262584 / 1
LCM(504,521) = 262584

Least Common Multiple (LCM) of 504 and 521 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 504 and 521. First we will calculate the prime factors of 504 and 521.

Prime Factorization of 504

Prime Factorization of 521

Now multiplying the highest exponent prime factors to calculate the LCM of 504 and 521.

LCM(504,521) = 2³ × 3² × 7¹ × 521¹
LCM(504,521) = 262584