What is the Least Common Multiple of 509 and 524?

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 509 and 524 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 509 and 524, than apply into the LCM equation.

GCF(509,524) = 1
LCM(509,524) = ( 509 × 524) / 1
LCM(509,524) = 266716 / 1
LCM(509,524) = 266716

Least Common Multiple (LCM) of 509 and 524 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 509 and 524. First we will calculate the prime factors of 509 and 524.

Prime Factorization of 509

Prime Factorization of 524

Now multiplying the highest exponent prime factors to calculate the LCM of 509 and 524.

LCM(509,524) = 509¹ × 2² × 131¹
LCM(509,524) = 266716