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What is the Least Common Multiple of 5727 and 5742?

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 5727 and 5742 is 10961478.

LCM(5727,5742) = 10961478

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Least Common Multiple of 5727 and 5742 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5727 and 5742, than apply into the LCM equation.

GCF(5727,5742) = 3
LCM(5727,5742) = ( 5727 × 5742) / 3
LCM(5727,5742) = 32884434 / 3
LCM(5727,5742) = 10961478

Least Common Multiple (LCM) of 5727 and 5742 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5727 and 5742. First we will calculate the prime factors of 5727 and 5742.

Prime Factorization of 5727

Prime factors of 5727 are 3, 23, 83. Prime factorization of 5727 in exponential form is:

5727 = 31 × 231 × 831

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

Now multiplying the highest exponent prime factors to calculate the LCM of 5727 and 5742.

LCM(5727,5742) = 32 × 231 × 831 × 21 × 111 × 291
LCM(5727,5742) = 10961478