What is the Least Common Multiple of 13674 and 13684?

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 13674 and 13684 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13674 and 13684, than apply into the LCM equation.

GCF(13674,13684) = 2
LCM(13674,13684) = ( 13674 × 13684) / 2
LCM(13674,13684) = 187115016 / 2
LCM(13674,13684) = 93557508

Least Common Multiple (LCM) of 13674 and 13684 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13674 and 13684. First we will calculate the prime factors of 13674 and 13684.

Prime Factorization of 13674

Prime Factorization of 13684

Now multiplying the highest exponent prime factors to calculate the LCM of 13674 and 13684.

LCM(13674,13684) = 2² × 3¹ × 43¹ × 53¹ × 11¹ × 311¹
LCM(13674,13684) = 93557508