What is the Least Common Multiple of 684 and 688?

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 684 and 688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 684 and 688, than apply into the LCM equation.

GCF(684,688) = 4
LCM(684,688) = ( 684 × 688) / 4
LCM(684,688) = 470592 / 4
LCM(684,688) = 117648

Least Common Multiple (LCM) of 684 and 688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 684 and 688. First we will calculate the prime factors of 684 and 688.

Prime Factorization of 684

Prime Factorization of 688

Now multiplying the highest exponent prime factors to calculate the LCM of 684 and 688.

LCM(684,688) = 2⁴ × 3² × 19¹ × 43¹
LCM(684,688) = 117648