What is the Least Common Multiple of 39990 and 40000?

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 39990 and 40000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39990 and 40000, than apply into the LCM equation.

GCF(39990,40000) = 10
LCM(39990,40000) = ( 39990 × 40000) / 10
LCM(39990,40000) = 1599600000 / 10
LCM(39990,40000) = 159960000

Least Common Multiple (LCM) of 39990 and 40000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39990 and 40000. First we will calculate the prime factors of 39990 and 40000.

Prime Factorization of 39990

Prime Factorization of 40000

Now multiplying the highest exponent prime factors to calculate the LCM of 39990 and 40000.

LCM(39990,40000) = 2⁶ × 3¹ × 5⁴ × 31¹ × 43¹
LCM(39990,40000) = 159960000