What is the Least Common Multiple of 39000 and 39013?

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 39000 and 39013 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39000 and 39013, than apply into the LCM equation.

GCF(39000,39013) = 13
LCM(39000,39013) = ( 39000 × 39013) / 13
LCM(39000,39013) = 1521507000 / 13
LCM(39000,39013) = 117039000

Least Common Multiple (LCM) of 39000 and 39013 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39000 and 39013. First we will calculate the prime factors of 39000 and 39013.

Prime Factorization of 39000

Prime Factorization of 39013

Now multiplying the highest exponent prime factors to calculate the LCM of 39000 and 39013.

LCM(39000,39013) = 2³ × 3¹ × 5³ × 13¹ × 3001¹
LCM(39000,39013) = 117039000