What is the Least Common Multiple of 38000 and 38016?

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 38000 and 38016 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38000 and 38016, than apply into the LCM equation.

GCF(38000,38016) = 16
LCM(38000,38016) = ( 38000 × 38016) / 16
LCM(38000,38016) = 1444608000 / 16
LCM(38000,38016) = 90288000

Least Common Multiple (LCM) of 38000 and 38016 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38000 and 38016. First we will calculate the prime factors of 38000 and 38016.

Prime Factorization of 38000

Prime Factorization of 38016

Now multiplying the highest exponent prime factors to calculate the LCM of 38000 and 38016.

LCM(38000,38016) = 2⁷ × 5³ × 19¹ × 3³ × 11¹
LCM(38000,38016) = 90288000