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What is the Least Common Multiple of 500 and 515?

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 500 and 515 is 51500.

LCM(500,515) = 51500

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Least Common Multiple of 500 and 515 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 500 and 515, than apply into the LCM equation.

GCF(500,515) = 5
LCM(500,515) = ( 500 × 515) / 5
LCM(500,515) = 257500 / 5
LCM(500,515) = 51500

Least Common Multiple (LCM) of 500 and 515 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 500 and 515. First we will calculate the prime factors of 500 and 515.

Prime Factorization of 500

Prime factors of 500 are 2, 5. Prime factorization of 500 in exponential form is:

500 = 22 × 53

Prime Factorization of 515

Prime factors of 515 are 5, 103. Prime factorization of 515 in exponential form is:

515 = 51 × 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 500 and 515.

LCM(500,515) = 22 × 53 × 1031
LCM(500,515) = 51500