What is the Least Common Multiple of 65000 and 65013?

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 65013 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 65013, than apply into the LCM equation.

GCF(65000,65013) = 13
LCM(65000,65013) = ( 65000 × 65013) / 13
LCM(65000,65013) = 4225845000 / 13
LCM(65000,65013) = 325065000

Least Common Multiple (LCM) of 65000 and 65013 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65000 and 65013. First we will calculate the prime factors of 65000 and 65013.

Prime Factorization of 65000

Prime Factorization of 65013

Now multiplying the highest exponent prime factors to calculate the LCM of 65000 and 65013.

LCM(65000,65013) = 2³ × 5⁴ × 13¹ × 3¹ × 1667¹
LCM(65000,65013) = 325065000