What is the Least Common Multiple of 509 and 516?

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 516 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 516, than apply into the LCM equation.

GCF(509,516) = 1
LCM(509,516) = ( 509 × 516) / 1
LCM(509,516) = 262644 / 1
LCM(509,516) = 262644

Least Common Multiple (LCM) of 509 and 516 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 509 and 516. First we will calculate the prime factors of 509 and 516.

Prime Factorization of 509

Prime Factorization of 516

Now multiplying the highest exponent prime factors to calculate the LCM of 509 and 516.

LCM(509,516) = 509¹ × 2² × 3¹ × 43¹
LCM(509,516) = 262644