What is the Least Common Multiple of 13440 and 13458?

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 13458 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 13458, than apply into the LCM equation.

GCF(13440,13458) = 6
LCM(13440,13458) = ( 13440 × 13458) / 6
LCM(13440,13458) = 180875520 / 6
LCM(13440,13458) = 30145920

Least Common Multiple (LCM) of 13440 and 13458 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13440 and 13458. First we will calculate the prime factors of 13440 and 13458.

Prime Factorization of 13440

Prime Factorization of 13458

Now multiplying the highest exponent prime factors to calculate the LCM of 13440 and 13458.

LCM(13440,13458) = 2⁷ × 3¹ × 5¹ × 7¹ × 2243¹
LCM(13440,13458) = 30145920