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What is the Least Common Multiple of 5296 and 5314?

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 5296 and 5314 is 14071472.

LCM(5296,5314) = 14071472

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Least Common Multiple of 5296 and 5314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5296 and 5314, than apply into the LCM equation.

GCF(5296,5314) = 2
LCM(5296,5314) = ( 5296 × 5314) / 2
LCM(5296,5314) = 28142944 / 2
LCM(5296,5314) = 14071472

Least Common Multiple (LCM) of 5296 and 5314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5296 and 5314. First we will calculate the prime factors of 5296 and 5314.

Prime Factorization of 5296

Prime factors of 5296 are 2, 331. Prime factorization of 5296 in exponential form is:

5296 = 24 × 3311

Prime Factorization of 5314

Prime factors of 5314 are 2, 2657. Prime factorization of 5314 in exponential form is:

5314 = 21 × 26571

Now multiplying the highest exponent prime factors to calculate the LCM of 5296 and 5314.

LCM(5296,5314) = 24 × 3311 × 26571
LCM(5296,5314) = 14071472