What is the Least Common Multiple of 13664 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 13664 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 13664 and 13680, than apply into the LCM equation.

GCF(13664,13680) = 16
LCM(13664,13680) = ( 13664 × 13680) / 16
LCM(13664,13680) = 186923520 / 16
LCM(13664,13680) = 11682720

Least Common Multiple (LCM) of 13664 and 13680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13664 and 13680. First we will calculate the prime factors of 13664 and 13680.

Prime Factorization of 13664

Prime Factorization of 13680

Now multiplying the highest exponent prime factors to calculate the LCM of 13664 and 13680.

LCM(13664,13680) = 2⁵ × 7¹ × 61¹ × 3² × 5¹ × 19¹
LCM(13664,13680) = 11682720