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What is the Least Common Multiple of 10004 and 10019?

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 10004 and 10019 is 100230076.

LCM(10004,10019) = 100230076

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Least Common Multiple of 10004 and 10019 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10004 and 10019, than apply into the LCM equation.

GCF(10004,10019) = 1
LCM(10004,10019) = ( 10004 × 10019) / 1
LCM(10004,10019) = 100230076 / 1
LCM(10004,10019) = 100230076

Least Common Multiple (LCM) of 10004 and 10019 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10004 and 10019. First we will calculate the prime factors of 10004 and 10019.

Prime Factorization of 10004

Prime factors of 10004 are 2, 41, 61. Prime factorization of 10004 in exponential form is:

10004 = 22 × 411 × 611

Prime Factorization of 10019

Prime factors of 10019 are 43, 233. Prime factorization of 10019 in exponential form is:

10019 = 431 × 2331

Now multiplying the highest exponent prime factors to calculate the LCM of 10004 and 10019.

LCM(10004,10019) = 22 × 411 × 611 × 431 × 2331
LCM(10004,10019) = 100230076