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What is the Least Common Multiple of 5730 and 5743?

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 5730 and 5743 is 32907390.

LCM(5730,5743) = 32907390

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Least Common Multiple of 5730 and 5743 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5730 and 5743, than apply into the LCM equation.

GCF(5730,5743) = 1
LCM(5730,5743) = ( 5730 × 5743) / 1
LCM(5730,5743) = 32907390 / 1
LCM(5730,5743) = 32907390

Least Common Multiple (LCM) of 5730 and 5743 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5730 and 5743. First we will calculate the prime factors of 5730 and 5743.

Prime Factorization of 5730

Prime factors of 5730 are 2, 3, 5, 191. Prime factorization of 5730 in exponential form is:

5730 = 21 × 31 × 51 × 1911

Prime Factorization of 5743

Prime factors of 5743 are 5743. Prime factorization of 5743 in exponential form is:

5743 = 57431

Now multiplying the highest exponent prime factors to calculate the LCM of 5730 and 5743.

LCM(5730,5743) = 21 × 31 × 51 × 1911 × 57431
LCM(5730,5743) = 32907390