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What is the Least Common Multiple of 12002 and 12010?

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 12002 and 12010 is 72072010.

LCM(12002,12010) = 72072010

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Least Common Multiple of 12002 and 12010 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12002 and 12010, than apply into the LCM equation.

GCF(12002,12010) = 2
LCM(12002,12010) = ( 12002 × 12010) / 2
LCM(12002,12010) = 144144020 / 2
LCM(12002,12010) = 72072010

Least Common Multiple (LCM) of 12002 and 12010 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12002 and 12010. First we will calculate the prime factors of 12002 and 12010.

Prime Factorization of 12002

Prime factors of 12002 are 2, 17, 353. Prime factorization of 12002 in exponential form is:

12002 = 21 × 171 × 3531

Prime Factorization of 12010

Prime factors of 12010 are 2, 5, 1201. Prime factorization of 12010 in exponential form is:

12010 = 21 × 51 × 12011

Now multiplying the highest exponent prime factors to calculate the LCM of 12002 and 12010.

LCM(12002,12010) = 21 × 171 × 3531 × 51 × 12011
LCM(12002,12010) = 72072010