What is the Least Common Multiple of 13125 and 13144?

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 13125 and 13144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13125 and 13144, than apply into the LCM equation.

GCF(13125,13144) = 1
LCM(13125,13144) = ( 13125 × 13144) / 1
LCM(13125,13144) = 172515000 / 1
LCM(13125,13144) = 172515000

Least Common Multiple (LCM) of 13125 and 13144 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13125 and 13144. First we will calculate the prime factors of 13125 and 13144.

Prime Factorization of 13125

Prime Factorization of 13144

Now multiplying the highest exponent prime factors to calculate the LCM of 13125 and 13144.

LCM(13125,13144) = 3¹ × 5⁴ × 7¹ × 2³ × 31¹ × 53¹
LCM(13125,13144) = 172515000