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What is the Least Common Multiple of 5712 and 5732?

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 5712 and 5732 is 8185296.

LCM(5712,5732) = 8185296

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Least Common Multiple of 5712 and 5732 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5712 and 5732, than apply into the LCM equation.

GCF(5712,5732) = 4
LCM(5712,5732) = ( 5712 × 5732) / 4
LCM(5712,5732) = 32741184 / 4
LCM(5712,5732) = 8185296

Least Common Multiple (LCM) of 5712 and 5732 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5712 and 5732. First we will calculate the prime factors of 5712 and 5732.

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

Prime Factorization of 5732

Prime factors of 5732 are 2, 1433. Prime factorization of 5732 in exponential form is:

5732 = 22 × 14331

Now multiplying the highest exponent prime factors to calculate the LCM of 5712 and 5732.

LCM(5712,5732) = 24 × 31 × 71 × 171 × 14331
LCM(5712,5732) = 8185296