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What is the Least Common Multiple of 42008 and 42024?

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 42008 and 42024 is 220668024.

LCM(42008,42024) = 220668024

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Least Common Multiple of 42008 and 42024 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42008 and 42024, than apply into the LCM equation.

GCF(42008,42024) = 8
LCM(42008,42024) = ( 42008 × 42024) / 8
LCM(42008,42024) = 1765344192 / 8
LCM(42008,42024) = 220668024

Least Common Multiple (LCM) of 42008 and 42024 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42008 and 42024. First we will calculate the prime factors of 42008 and 42024.

Prime Factorization of 42008

Prime factors of 42008 are 2, 59, 89. Prime factorization of 42008 in exponential form is:

42008 = 23 × 591 × 891

Prime Factorization of 42024

Prime factors of 42024 are 2, 3, 17, 103. Prime factorization of 42024 in exponential form is:

42024 = 23 × 31 × 171 × 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 42008 and 42024.

LCM(42008,42024) = 23 × 591 × 891 × 31 × 171 × 1031
LCM(42008,42024) = 220668024