What is the Least Common Multiple of 514 and 528?

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 514 and 528 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 514 and 528, than apply into the LCM equation.

GCF(514,528) = 2
LCM(514,528) = ( 514 × 528) / 2
LCM(514,528) = 271392 / 2
LCM(514,528) = 135696

Least Common Multiple (LCM) of 514 and 528 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 514 and 528. First we will calculate the prime factors of 514 and 528.

Prime Factorization of 514

Prime Factorization of 528

Now multiplying the highest exponent prime factors to calculate the LCM of 514 and 528.

LCM(514,528) = 2⁴ × 257¹ × 3¹ × 11¹
LCM(514,528) = 135696