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What is the Least Common Multiple of 13005 and 13010?

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 13005 and 13010 is 33839010.

LCM(13005,13010) = 33839010

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Least Common Multiple of 13005 and 13010 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13005 and 13010, than apply into the LCM equation.

GCF(13005,13010) = 5
LCM(13005,13010) = ( 13005 × 13010) / 5
LCM(13005,13010) = 169195050 / 5
LCM(13005,13010) = 33839010

Least Common Multiple (LCM) of 13005 and 13010 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13005 and 13010. First we will calculate the prime factors of 13005 and 13010.

Prime Factorization of 13005

Prime factors of 13005 are 3, 5, 17. Prime factorization of 13005 in exponential form is:

13005 = 32 × 51 × 172

Prime Factorization of 13010

Prime factors of 13010 are 2, 5, 1301. Prime factorization of 13010 in exponential form is:

13010 = 21 × 51 × 13011

Now multiplying the highest exponent prime factors to calculate the LCM of 13005 and 13010.

LCM(13005,13010) = 32 × 51 × 172 × 21 × 13011
LCM(13005,13010) = 33839010