What is the Least Common Multiple of 13584 and 13602?

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 13602 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 13602, than apply into the LCM equation.

GCF(13584,13602) = 6
LCM(13584,13602) = ( 13584 × 13602) / 6
LCM(13584,13602) = 184769568 / 6
LCM(13584,13602) = 30794928

Least Common Multiple (LCM) of 13584 and 13602 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13584 and 13602. First we will calculate the prime factors of 13584 and 13602.

Prime Factorization of 13584

Prime Factorization of 13602

Now multiplying the highest exponent prime factors to calculate the LCM of 13584 and 13602.

LCM(13584,13602) = 2⁴ × 3¹ × 283¹ × 2267¹
LCM(13584,13602) = 30794928