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What is the Least Common Multiple of 7008 and 7016?

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 7008 and 7016 is 6146016.

LCM(7008,7016) = 6146016

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Least Common Multiple of 7008 and 7016 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7008 and 7016, than apply into the LCM equation.

GCF(7008,7016) = 8
LCM(7008,7016) = ( 7008 × 7016) / 8
LCM(7008,7016) = 49168128 / 8
LCM(7008,7016) = 6146016

Least Common Multiple (LCM) of 7008 and 7016 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7008 and 7016. First we will calculate the prime factors of 7008 and 7016.

Prime Factorization of 7008

Prime factors of 7008 are 2, 3, 73. Prime factorization of 7008 in exponential form is:

7008 = 25 × 31 × 731

Prime Factorization of 7016

Prime factors of 7016 are 2, 877. Prime factorization of 7016 in exponential form is:

7016 = 23 × 8771

Now multiplying the highest exponent prime factors to calculate the LCM of 7008 and 7016.

LCM(7008,7016) = 25 × 31 × 731 × 8771
LCM(7008,7016) = 6146016