What is the Least Common Multiple of 9990 and 10000?

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 9990 and 10000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9990 and 10000, than apply into the LCM equation.

GCF(9990,10000) = 10
LCM(9990,10000) = ( 9990 × 10000) / 10
LCM(9990,10000) = 99900000 / 10
LCM(9990,10000) = 9990000

Least Common Multiple (LCM) of 9990 and 10000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9990 and 10000. First we will calculate the prime factors of 9990 and 10000.

Prime Factorization of 9990

Prime Factorization of 10000

Now multiplying the highest exponent prime factors to calculate the LCM of 9990 and 10000.

LCM(9990,10000) = 2⁴ × 3³ × 5⁴ × 37¹
LCM(9990,10000) = 9990000