What is the Least Common Multiple of 13563 and 13578?

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 13563 and 13578 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13563 and 13578, than apply into the LCM equation.

GCF(13563,13578) = 3
LCM(13563,13578) = ( 13563 × 13578) / 3
LCM(13563,13578) = 184158414 / 3
LCM(13563,13578) = 61386138

Least Common Multiple (LCM) of 13563 and 13578 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13563 and 13578. First we will calculate the prime factors of 13563 and 13578.

Prime Factorization of 13563

Prime Factorization of 13578

Now multiplying the highest exponent prime factors to calculate the LCM of 13563 and 13578.

LCM(13563,13578) = 3² × 11¹ × 137¹ × 2¹ × 31¹ × 73¹
LCM(13563,13578) = 61386138