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What is the Least Common Multiple of 27000 and 27013?

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 27000 and 27013 is 729351000.

LCM(27000,27013) = 729351000

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Least Common Multiple of 27000 and 27013 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27000 and 27013, than apply into the LCM equation.

GCF(27000,27013) = 1
LCM(27000,27013) = ( 27000 × 27013) / 1
LCM(27000,27013) = 729351000 / 1
LCM(27000,27013) = 729351000

Least Common Multiple (LCM) of 27000 and 27013 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27000 and 27013. First we will calculate the prime factors of 27000 and 27013.

Prime Factorization of 27000

Prime factors of 27000 are 2, 3, 5. Prime factorization of 27000 in exponential form is:

27000 = 23 × 33 × 53

Prime Factorization of 27013

Prime factors of 27013 are 7, 17, 227. Prime factorization of 27013 in exponential form is:

27013 = 71 × 171 × 2271

Now multiplying the highest exponent prime factors to calculate the LCM of 27000 and 27013.

LCM(27000,27013) = 23 × 33 × 53 × 71 × 171 × 2271
LCM(27000,27013) = 729351000