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What is the Least Common Multiple of 2006 and 2019?

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 2006 and 2019 is 4050114.

LCM(2006,2019) = 4050114

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Least Common Multiple of 2006 and 2019 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2006 and 2019, than apply into the LCM equation.

GCF(2006,2019) = 1
LCM(2006,2019) = ( 2006 × 2019) / 1
LCM(2006,2019) = 4050114 / 1
LCM(2006,2019) = 4050114

Least Common Multiple (LCM) of 2006 and 2019 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2006 and 2019. First we will calculate the prime factors of 2006 and 2019.

Prime Factorization of 2006

Prime factors of 2006 are 2, 17, 59. Prime factorization of 2006 in exponential form is:

2006 = 21 × 171 × 591

Prime Factorization of 2019

Prime factors of 2019 are 3, 673. Prime factorization of 2019 in exponential form is:

2019 = 31 × 6731

Now multiplying the highest exponent prime factors to calculate the LCM of 2006 and 2019.

LCM(2006,2019) = 21 × 171 × 591 × 31 × 6731
LCM(2006,2019) = 4050114