What is the Least Common Multiple of 4500 and 4509?

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 4500 and 4509 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4500 and 4509, than apply into the LCM equation.

GCF(4500,4509) = 9
LCM(4500,4509) = ( 4500 × 4509) / 9
LCM(4500,4509) = 20290500 / 9
LCM(4500,4509) = 2254500

Least Common Multiple (LCM) of 4500 and 4509 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 4500 and 4509. First we will calculate the prime factors of 4500 and 4509.

Prime Factorization of 4500

Prime Factorization of 4509

Now multiplying the highest exponent prime factors to calculate the LCM of 4500 and 4509.

LCM(4500,4509) = 2² × 3³ × 5³ × 167¹
LCM(4500,4509) = 2254500