What is the Least Common Multiple of 38985 and 39000?

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 38985 and 39000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38985 and 39000, than apply into the LCM equation.

GCF(38985,39000) = 15
LCM(38985,39000) = ( 38985 × 39000) / 15
LCM(38985,39000) = 1520415000 / 15
LCM(38985,39000) = 101361000

Least Common Multiple (LCM) of 38985 and 39000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38985 and 39000. First we will calculate the prime factors of 38985 and 39000.

Prime Factorization of 38985

Prime Factorization of 39000

Now multiplying the highest exponent prime factors to calculate the LCM of 38985 and 39000.

LCM(38985,39000) = 3¹ × 5³ × 23¹ × 113¹ × 2³ × 13¹
LCM(38985,39000) = 101361000