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What is the Least Common Multiple of 28000 and 28009?

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 28000 and 28009 is 784252000.

LCM(28000,28009) = 784252000

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Least Common Multiple of 28000 and 28009 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 28000 and 28009, than apply into the LCM equation.

GCF(28000,28009) = 1
LCM(28000,28009) = ( 28000 × 28009) / 1
LCM(28000,28009) = 784252000 / 1
LCM(28000,28009) = 784252000

Least Common Multiple (LCM) of 28000 and 28009 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 28000 and 28009. First we will calculate the prime factors of 28000 and 28009.

Prime Factorization of 28000

Prime factors of 28000 are 2, 5, 7. Prime factorization of 28000 in exponential form is:

28000 = 25 × 53 × 71

Prime Factorization of 28009

Prime factors of 28009 are 37, 757. Prime factorization of 28009 in exponential form is:

28009 = 371 × 7571

Now multiplying the highest exponent prime factors to calculate the LCM of 28000 and 28009.

LCM(28000,28009) = 25 × 53 × 71 × 371 × 7571
LCM(28000,28009) = 784252000