What is the Least Common Multiple of 13665 and 13680?

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 13665 and 13680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13665 and 13680, than apply into the LCM equation.

GCF(13665,13680) = 15
LCM(13665,13680) = ( 13665 × 13680) / 15
LCM(13665,13680) = 186937200 / 15
LCM(13665,13680) = 12462480

Least Common Multiple (LCM) of 13665 and 13680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13665 and 13680. First we will calculate the prime factors of 13665 and 13680.

Prime Factorization of 13665

Prime Factorization of 13680

Now multiplying the highest exponent prime factors to calculate the LCM of 13665 and 13680.

LCM(13665,13680) = 3² × 5¹ × 911¹ × 2⁴ × 19¹
LCM(13665,13680) = 12462480