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What is the Least Common Multiple of 10001 and 10014?

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 10001 and 10014 is 100150014.

LCM(10001,10014) = 100150014

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Least Common Multiple of 10001 and 10014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10001 and 10014, than apply into the LCM equation.

GCF(10001,10014) = 1
LCM(10001,10014) = ( 10001 × 10014) / 1
LCM(10001,10014) = 100150014 / 1
LCM(10001,10014) = 100150014

Least Common Multiple (LCM) of 10001 and 10014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10001 and 10014. First we will calculate the prime factors of 10001 and 10014.

Prime Factorization of 10001

Prime factors of 10001 are 73, 137. Prime factorization of 10001 in exponential form is:

10001 = 731 × 1371

Prime Factorization of 10014

Prime factors of 10014 are 2, 3, 1669. Prime factorization of 10014 in exponential form is:

10014 = 21 × 31 × 16691

Now multiplying the highest exponent prime factors to calculate the LCM of 10001 and 10014.

LCM(10001,10014) = 731 × 1371 × 21 × 31 × 16691
LCM(10001,10014) = 100150014