What is the Least Common Multiple of 13686 and 13704?

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 13686 and 13704 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13686 and 13704, than apply into the LCM equation.

GCF(13686,13704) = 6
LCM(13686,13704) = ( 13686 × 13704) / 6
LCM(13686,13704) = 187552944 / 6
LCM(13686,13704) = 31258824

Least Common Multiple (LCM) of 13686 and 13704 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13686 and 13704. First we will calculate the prime factors of 13686 and 13704.

Prime Factorization of 13686

Prime Factorization of 13704

Now multiplying the highest exponent prime factors to calculate the LCM of 13686 and 13704.

LCM(13686,13704) = 2³ × 3¹ × 2281¹ × 571¹
LCM(13686,13704) = 31258824