What is the Least Common Multiple of 13680 and 13694?

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 13680 and 13694 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13680 and 13694, than apply into the LCM equation.

GCF(13680,13694) = 2
LCM(13680,13694) = ( 13680 × 13694) / 2
LCM(13680,13694) = 187333920 / 2
LCM(13680,13694) = 93666960

Least Common Multiple (LCM) of 13680 and 13694 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13680 and 13694. First we will calculate the prime factors of 13680 and 13694.

Prime Factorization of 13680

Prime Factorization of 13694

Now multiplying the highest exponent prime factors to calculate the LCM of 13680 and 13694.

LCM(13680,13694) = 2⁴ × 3² × 5¹ × 19¹ × 41¹ × 167¹
LCM(13680,13694) = 93666960