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What is the Least Common Multiple of 8007 and 8025?

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 8007 and 8025 is 21418725.

LCM(8007,8025) = 21418725

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Least Common Multiple of 8007 and 8025 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8007 and 8025, than apply into the LCM equation.

GCF(8007,8025) = 3
LCM(8007,8025) = ( 8007 × 8025) / 3
LCM(8007,8025) = 64256175 / 3
LCM(8007,8025) = 21418725

Least Common Multiple (LCM) of 8007 and 8025 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8007 and 8025. First we will calculate the prime factors of 8007 and 8025.

Prime Factorization of 8007

Prime factors of 8007 are 3, 17, 157. Prime factorization of 8007 in exponential form is:

8007 = 31 × 171 × 1571

Prime Factorization of 8025

Prime factors of 8025 are 3, 5, 107. Prime factorization of 8025 in exponential form is:

8025 = 31 × 52 × 1071

Now multiplying the highest exponent prime factors to calculate the LCM of 8007 and 8025.

LCM(8007,8025) = 31 × 171 × 1571 × 52 × 1071
LCM(8007,8025) = 21418725