What is the Least Common Multiple of 306 and 310?

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 306 and 310 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 306 and 310, than apply into the LCM equation.

GCF(306,310) = 2
LCM(306,310) = ( 306 × 310) / 2
LCM(306,310) = 94860 / 2
LCM(306,310) = 47430

Least Common Multiple (LCM) of 306 and 310 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 306 and 310. First we will calculate the prime factors of 306 and 310.

Prime Factorization of 306

Prime Factorization of 310

Now multiplying the highest exponent prime factors to calculate the LCM of 306 and 310.

LCM(306,310) = 2¹ × 3² × 17¹ × 5¹ × 31¹
LCM(306,310) = 47430