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What is the Least Common Multiple of 10000 and 10020?

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 10000 and 10020 is 5010000.

LCM(10000,10020) = 5010000

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Least Common Multiple of 10000 and 10020 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10000 and 10020, than apply into the LCM equation.

GCF(10000,10020) = 20
LCM(10000,10020) = ( 10000 × 10020) / 20
LCM(10000,10020) = 100200000 / 20
LCM(10000,10020) = 5010000

Least Common Multiple (LCM) of 10000 and 10020 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10000 and 10020. First we will calculate the prime factors of 10000 and 10020.

Prime Factorization of 10000

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

10000 = 24 × 54

Prime Factorization of 10020

Prime factors of 10020 are 2, 3, 5, 167. Prime factorization of 10020 in exponential form is:

10020 = 22 × 31 × 51 × 1671

Now multiplying the highest exponent prime factors to calculate the LCM of 10000 and 10020.

LCM(10000,10020) = 24 × 54 × 31 × 1671
LCM(10000,10020) = 5010000