What is the Least Common Multiple of 37980 and 38000?

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 37980 and 38000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37980 and 38000, than apply into the LCM equation.

GCF(37980,38000) = 20
LCM(37980,38000) = ( 37980 × 38000) / 20
LCM(37980,38000) = 1443240000 / 20
LCM(37980,38000) = 72162000

Least Common Multiple (LCM) of 37980 and 38000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37980 and 38000. First we will calculate the prime factors of 37980 and 38000.

Prime Factorization of 37980

Prime Factorization of 38000

Now multiplying the highest exponent prime factors to calculate the LCM of 37980 and 38000.

LCM(37980,38000) = 2⁴ × 3² × 5³ × 211¹ × 19¹
LCM(37980,38000) = 72162000