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What is the Least Common Multiple of 5685 and 5704?

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 5704 is 32427240.

LCM(5685,5704) = 32427240

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Least Common Multiple of 5685 and 5704 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 5704, than apply into the LCM equation.

GCF(5685,5704) = 1
LCM(5685,5704) = ( 5685 × 5704) / 1
LCM(5685,5704) = 32427240 / 1
LCM(5685,5704) = 32427240

Least Common Multiple (LCM) of 5685 and 5704 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5685 and 5704. First we will calculate the prime factors of 5685 and 5704.

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 5704

Prime factors of 5704 are 2, 23, 31. Prime factorization of 5704 in exponential form is:

5704 = 23 × 231 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 5685 and 5704.

LCM(5685,5704) = 31 × 51 × 3791 × 23 × 231 × 311
LCM(5685,5704) = 32427240