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What is the Least Common Multiple of 2007 and 2024?

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 2007 and 2024 is 4062168.

LCM(2007,2024) = 4062168

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Least Common Multiple of 2007 and 2024 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2007 and 2024, than apply into the LCM equation.

GCF(2007,2024) = 1
LCM(2007,2024) = ( 2007 × 2024) / 1
LCM(2007,2024) = 4062168 / 1
LCM(2007,2024) = 4062168

Least Common Multiple (LCM) of 2007 and 2024 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2007 and 2024. First we will calculate the prime factors of 2007 and 2024.

Prime Factorization of 2007

Prime factors of 2007 are 3, 223. Prime factorization of 2007 in exponential form is:

2007 = 32 × 2231

Prime Factorization of 2024

Prime factors of 2024 are 2, 11, 23. Prime factorization of 2024 in exponential form is:

2024 = 23 × 111 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 2007 and 2024.

LCM(2007,2024) = 32 × 2231 × 23 × 111 × 231
LCM(2007,2024) = 4062168