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What is the Least Common Multiple of 5685 and 5700?

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 5685 and 5700 is 2160300.

LCM(5685,5700) = 2160300

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Least Common Multiple of 5685 and 5700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5685 and 5700, than apply into the LCM equation.

GCF(5685,5700) = 15
LCM(5685,5700) = ( 5685 × 5700) / 15
LCM(5685,5700) = 32404500 / 15
LCM(5685,5700) = 2160300

Least Common Multiple (LCM) of 5685 and 5700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5685 and 5700. First we will calculate the prime factors of 5685 and 5700.

Prime Factorization of 5685

Prime factors of 5685 are 3, 5, 379. Prime factorization of 5685 in exponential form is:

5685 = 31 × 51 × 3791

Prime Factorization of 5700

Prime factors of 5700 are 2, 3, 5, 19. Prime factorization of 5700 in exponential form is:

5700 = 22 × 31 × 52 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 5685 and 5700.

LCM(5685,5700) = 31 × 52 × 3791 × 22 × 191
LCM(5685,5700) = 2160300