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What is the Least Common Multiple of 8004 and 8014?

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 8004 and 8014 is 32072028.

LCM(8004,8014) = 32072028

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Least Common Multiple of 8004 and 8014 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8004 and 8014, than apply into the LCM equation.

GCF(8004,8014) = 2
LCM(8004,8014) = ( 8004 × 8014) / 2
LCM(8004,8014) = 64144056 / 2
LCM(8004,8014) = 32072028

Least Common Multiple (LCM) of 8004 and 8014 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8004 and 8014. First we will calculate the prime factors of 8004 and 8014.

Prime Factorization of 8004

Prime factors of 8004 are 2, 3, 23, 29. Prime factorization of 8004 in exponential form is:

8004 = 22 × 31 × 231 × 291

Prime Factorization of 8014

Prime factors of 8014 are 2, 4007. Prime factorization of 8014 in exponential form is:

8014 = 21 × 40071

Now multiplying the highest exponent prime factors to calculate the LCM of 8004 and 8014.

LCM(8004,8014) = 22 × 31 × 231 × 291 × 40071
LCM(8004,8014) = 32072028