What is the Least Common Multiple of 65000 and 65009?

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 65000 and 65009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65000 and 65009, than apply into the LCM equation.

GCF(65000,65009) = 1
LCM(65000,65009) = ( 65000 × 65009) / 1
LCM(65000,65009) = 4225585000 / 1
LCM(65000,65009) = 4225585000

Least Common Multiple (LCM) of 65000 and 65009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65000 and 65009. First we will calculate the prime factors of 65000 and 65009.

Prime Factorization of 65000

Prime Factorization of 65009

Now multiplying the highest exponent prime factors to calculate the LCM of 65000 and 65009.

LCM(65000,65009) = 2³ × 5⁴ × 13¹ × 7¹ × 37¹ × 251¹
LCM(65000,65009) = 4225585000