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What is the Least Common Multiple of 2008 and 2020?

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 2020 is 1014040.

LCM(2008,2020) = 1014040

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Least Common Multiple of 2008 and 2020 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 2020, than apply into the LCM equation.

GCF(2008,2020) = 4
LCM(2008,2020) = ( 2008 × 2020) / 4
LCM(2008,2020) = 4056160 / 4
LCM(2008,2020) = 1014040

Least Common Multiple (LCM) of 2008 and 2020 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2008 and 2020. First we will calculate the prime factors of 2008 and 2020.

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 2020

Prime factors of 2020 are 2, 5, 101. Prime factorization of 2020 in exponential form is:

2020 = 22 × 51 × 1011

Now multiplying the highest exponent prime factors to calculate the LCM of 2008 and 2020.

LCM(2008,2020) = 23 × 2511 × 51 × 1011
LCM(2008,2020) = 1014040