What is the Least Common Multiple of 6500 and 6509?

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 6500 and 6509 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6500 and 6509, than apply into the LCM equation.

GCF(6500,6509) = 1
LCM(6500,6509) = ( 6500 × 6509) / 1
LCM(6500,6509) = 42308500 / 1
LCM(6500,6509) = 42308500

Least Common Multiple (LCM) of 6500 and 6509 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6500 and 6509. First we will calculate the prime factors of 6500 and 6509.

Prime Factorization of 6500

Prime Factorization of 6509

Now multiplying the highest exponent prime factors to calculate the LCM of 6500 and 6509.

LCM(6500,6509) = 2² × 5³ × 13¹ × 23¹ × 283¹
LCM(6500,6509) = 42308500