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What is the Least Common Multiple of 2008 and 2015?

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 2008 and 2015 is 4046120.

LCM(2008,2015) = 4046120

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Least Common Multiple of 2008 and 2015 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2008 and 2015, than apply into the LCM equation.

GCF(2008,2015) = 1
LCM(2008,2015) = ( 2008 × 2015) / 1
LCM(2008,2015) = 4046120 / 1
LCM(2008,2015) = 4046120

Least Common Multiple (LCM) of 2008 and 2015 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2008 and 2015. First we will calculate the prime factors of 2008 and 2015.

Prime Factorization of 2008

Prime factors of 2008 are 2, 251. Prime factorization of 2008 in exponential form is:

2008 = 23 × 2511

Prime Factorization of 2015

Prime factors of 2015 are 5, 13, 31. Prime factorization of 2015 in exponential form is:

2015 = 51 × 131 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 2008 and 2015.

LCM(2008,2015) = 23 × 2511 × 51 × 131 × 311
LCM(2008,2015) = 4046120