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What is the Least Common Multiple of 13006 and 13013?

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 13006 and 13013 is 24178154.

LCM(13006,13013) = 24178154

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Least Common Multiple of 13006 and 13013 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13006 and 13013, than apply into the LCM equation.

GCF(13006,13013) = 7
LCM(13006,13013) = ( 13006 × 13013) / 7
LCM(13006,13013) = 169247078 / 7
LCM(13006,13013) = 24178154

Least Common Multiple (LCM) of 13006 and 13013 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13006 and 13013. First we will calculate the prime factors of 13006 and 13013.

Prime Factorization of 13006

Prime factors of 13006 are 2, 7, 929. Prime factorization of 13006 in exponential form is:

13006 = 21 × 71 × 9291

Prime Factorization of 13013

Prime factors of 13013 are 7, 11, 13. Prime factorization of 13013 in exponential form is:

13013 = 71 × 111 × 132

Now multiplying the highest exponent prime factors to calculate the LCM of 13006 and 13013.

LCM(13006,13013) = 21 × 71 × 9291 × 111 × 132
LCM(13006,13013) = 24178154