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What is the Least Common Multiple of 5742 and 5758?

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 5742 and 5758 is 16531218.

LCM(5742,5758) = 16531218

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Least Common Multiple of 5742 and 5758 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5742 and 5758, than apply into the LCM equation.

GCF(5742,5758) = 2
LCM(5742,5758) = ( 5742 × 5758) / 2
LCM(5742,5758) = 33062436 / 2
LCM(5742,5758) = 16531218

Least Common Multiple (LCM) of 5742 and 5758 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5742 and 5758. First we will calculate the prime factors of 5742 and 5758.

Prime Factorization of 5742

Prime factors of 5742 are 2, 3, 11, 29. Prime factorization of 5742 in exponential form is:

5742 = 21 × 32 × 111 × 291

Prime Factorization of 5758

Prime factors of 5758 are 2, 2879. Prime factorization of 5758 in exponential form is:

5758 = 21 × 28791

Now multiplying the highest exponent prime factors to calculate the LCM of 5742 and 5758.

LCM(5742,5758) = 21 × 32 × 111 × 291 × 28791
LCM(5742,5758) = 16531218