What is the Least Common Multiple of 514 and 522?

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 522 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 522, than apply into the LCM equation.

GCF(514,522) = 2
LCM(514,522) = ( 514 × 522) / 2
LCM(514,522) = 268308 / 2
LCM(514,522) = 134154

Least Common Multiple (LCM) of 514 and 522 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 514 and 522. First we will calculate the prime factors of 514 and 522.

Prime Factorization of 514

Prime Factorization of 522

Now multiplying the highest exponent prime factors to calculate the LCM of 514 and 522.

LCM(514,522) = 2¹ × 257¹ × 3² × 29¹
LCM(514,522) = 134154