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What is the Least Common Multiple of 5692 and 5712?

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 5692 and 5712 is 8128176.

LCM(5692,5712) = 8128176

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Least Common Multiple of 5692 and 5712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5692 and 5712, than apply into the LCM equation.

GCF(5692,5712) = 4
LCM(5692,5712) = ( 5692 × 5712) / 4
LCM(5692,5712) = 32512704 / 4
LCM(5692,5712) = 8128176

Least Common Multiple (LCM) of 5692 and 5712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5692 and 5712. First we will calculate the prime factors of 5692 and 5712.

Prime Factorization of 5692

Prime factors of 5692 are 2, 1423. Prime factorization of 5692 in exponential form is:

5692 = 22 × 14231

Prime Factorization of 5712

Prime factors of 5712 are 2, 3, 7, 17. Prime factorization of 5712 in exponential form is:

5712 = 24 × 31 × 71 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 5692 and 5712.

LCM(5692,5712) = 24 × 14231 × 31 × 71 × 171
LCM(5692,5712) = 8128176