What is the Least Common Multiple of 13440 and 13460?

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 13440 and 13460 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13440 and 13460, than apply into the LCM equation.

GCF(13440,13460) = 20
LCM(13440,13460) = ( 13440 × 13460) / 20
LCM(13440,13460) = 180902400 / 20
LCM(13440,13460) = 9045120

Least Common Multiple (LCM) of 13440 and 13460 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13440 and 13460. First we will calculate the prime factors of 13440 and 13460.

Prime Factorization of 13440

Prime Factorization of 13460

Now multiplying the highest exponent prime factors to calculate the LCM of 13440 and 13460.

LCM(13440,13460) = 2⁷ × 3¹ × 5¹ × 7¹ × 673¹
LCM(13440,13460) = 9045120