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What is the Least Common Multiple of 5750 and 5764?

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 5750 and 5764 is 16571500.

LCM(5750,5764) = 16571500

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Least Common Multiple of 5750 and 5764 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5750 and 5764, than apply into the LCM equation.

GCF(5750,5764) = 2
LCM(5750,5764) = ( 5750 × 5764) / 2
LCM(5750,5764) = 33143000 / 2
LCM(5750,5764) = 16571500

Least Common Multiple (LCM) of 5750 and 5764 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5750 and 5764. First we will calculate the prime factors of 5750 and 5764.

Prime Factorization of 5750

Prime factors of 5750 are 2, 5, 23. Prime factorization of 5750 in exponential form is:

5750 = 21 × 53 × 231

Prime Factorization of 5764

Prime factors of 5764 are 2, 11, 131. Prime factorization of 5764 in exponential form is:

5764 = 22 × 111 × 1311

Now multiplying the highest exponent prime factors to calculate the LCM of 5750 and 5764.

LCM(5750,5764) = 22 × 53 × 231 × 111 × 1311
LCM(5750,5764) = 16571500