What is the Least Common Multiple of 13500 and 13509?

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 13500 and 13509 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13500 and 13509, than apply into the LCM equation.

GCF(13500,13509) = 9
LCM(13500,13509) = ( 13500 × 13509) / 9
LCM(13500,13509) = 182371500 / 9
LCM(13500,13509) = 20263500

Least Common Multiple (LCM) of 13500 and 13509 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13500 and 13509. First we will calculate the prime factors of 13500 and 13509.

Prime Factorization of 13500

Prime Factorization of 13509

Now multiplying the highest exponent prime factors to calculate the LCM of 13500 and 13509.

LCM(13500,13509) = 2² × 3³ × 5³ × 19¹ × 79¹
LCM(13500,13509) = 20263500