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What is the Least Common Multiple of 10002 and 10013?

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 10002 and 10013 is 100150026.

LCM(10002,10013) = 100150026

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Least Common Multiple of 10002 and 10013 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10002 and 10013, than apply into the LCM equation.

GCF(10002,10013) = 1
LCM(10002,10013) = ( 10002 × 10013) / 1
LCM(10002,10013) = 100150026 / 1
LCM(10002,10013) = 100150026

Least Common Multiple (LCM) of 10002 and 10013 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10002 and 10013. First we will calculate the prime factors of 10002 and 10013.

Prime Factorization of 10002

Prime factors of 10002 are 2, 3, 1667. Prime factorization of 10002 in exponential form is:

10002 = 21 × 31 × 16671

Prime Factorization of 10013

Prime factors of 10013 are 17, 19, 31. Prime factorization of 10013 in exponential form is:

10013 = 171 × 191 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 10002 and 10013.

LCM(10002,10013) = 21 × 31 × 16671 × 171 × 191 × 311
LCM(10002,10013) = 100150026