What is the Least Common Multiple of 13584 and 13590?

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 13584 and 13590 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13584 and 13590, than apply into the LCM equation.

GCF(13584,13590) = 6
LCM(13584,13590) = ( 13584 × 13590) / 6
LCM(13584,13590) = 184606560 / 6
LCM(13584,13590) = 30767760

Least Common Multiple (LCM) of 13584 and 13590 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13584 and 13590. First we will calculate the prime factors of 13584 and 13590.

Prime Factorization of 13584

Prime Factorization of 13590

Now multiplying the highest exponent prime factors to calculate the LCM of 13584 and 13590.

LCM(13584,13590) = 2⁴ × 3² × 283¹ × 5¹ × 151¹
LCM(13584,13590) = 30767760