What is the Least Common Multiple of 513 and 523?

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 513 and 523 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 513 and 523, than apply into the LCM equation.

GCF(513,523) = 1
LCM(513,523) = ( 513 × 523) / 1
LCM(513,523) = 268299 / 1
LCM(513,523) = 268299

Least Common Multiple (LCM) of 513 and 523 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 513 and 523. First we will calculate the prime factors of 513 and 523.

Prime Factorization of 513

Prime Factorization of 523

Now multiplying the highest exponent prime factors to calculate the LCM of 513 and 523.

LCM(513,523) = 3³ × 19¹ × 523¹
LCM(513,523) = 268299