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What is the Least Common Multiple of 9996 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 (LCM) of 9996 and 10000 is 24990000.

LCM(9996,10000) = 24990000

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Least Common Multiple of 9996 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 9996 and 10000, than apply into the LCM equation.

GCF(9996,10000) = 4
LCM(9996,10000) = ( 9996 × 10000) / 4
LCM(9996,10000) = 99960000 / 4
LCM(9996,10000) = 24990000

Least Common Multiple (LCM) of 9996 and 10000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9996 and 10000. First we will calculate the prime factors of 9996 and 10000.

Prime Factorization of 9996

Prime factors of 9996 are 2, 3, 7, 17. Prime factorization of 9996 in exponential form is:

9996 = 22 × 31 × 72 × 171

Prime Factorization of 10000

Prime factors of 10000 are 2, 5. Prime factorization of 10000 in exponential form is:

10000 = 24 × 54

Now multiplying the highest exponent prime factors to calculate the LCM of 9996 and 10000.

LCM(9996,10000) = 24 × 31 × 72 × 171 × 54
LCM(9996,10000) = 24990000