What is the Least Common Multiple of 38000 and 38008?

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 38008 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 38008, than apply into the LCM equation.

GCF(38000,38008) = 8
LCM(38000,38008) = ( 38000 × 38008) / 8
LCM(38000,38008) = 1444304000 / 8
LCM(38000,38008) = 180538000

Least Common Multiple (LCM) of 38000 and 38008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38000 and 38008. First we will calculate the prime factors of 38000 and 38008.

Prime Factorization of 38000

Prime Factorization of 38008

Now multiplying the highest exponent prime factors to calculate the LCM of 38000 and 38008.

LCM(38000,38008) = 2⁴ × 5³ × 19¹ × 4751¹
LCM(38000,38008) = 180538000