What is the Least Common Multiple of 13680 and 13689?

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 13689 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 13689, than apply into the LCM equation.

GCF(13680,13689) = 9
LCM(13680,13689) = ( 13680 × 13689) / 9
LCM(13680,13689) = 187265520 / 9
LCM(13680,13689) = 20807280

Least Common Multiple (LCM) of 13680 and 13689 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13680 and 13689. First we will calculate the prime factors of 13680 and 13689.

Prime Factorization of 13680

Prime Factorization of 13689

Now multiplying the highest exponent prime factors to calculate the LCM of 13680 and 13689.

LCM(13680,13689) = 2⁴ × 3⁴ × 5¹ × 19¹ × 13²
LCM(13680,13689) = 20807280