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What is the Least Common Multiple of 27710 and 27727?

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 27710 and 27727 is 45195010.

LCM(27710,27727) = 45195010

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Least Common Multiple of 27710 and 27727 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27710 and 27727, than apply into the LCM equation.

GCF(27710,27727) = 17
LCM(27710,27727) = ( 27710 × 27727) / 17
LCM(27710,27727) = 768315170 / 17
LCM(27710,27727) = 45195010

Least Common Multiple (LCM) of 27710 and 27727 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27710 and 27727. First we will calculate the prime factors of 27710 and 27727.

Prime Factorization of 27710

Prime factors of 27710 are 2, 5, 17, 163. Prime factorization of 27710 in exponential form is:

27710 = 21 × 51 × 171 × 1631

Prime Factorization of 27727

Prime factors of 27727 are 7, 17, 233. Prime factorization of 27727 in exponential form is:

27727 = 71 × 171 × 2331

Now multiplying the highest exponent prime factors to calculate the LCM of 27710 and 27727.

LCM(27710,27727) = 21 × 51 × 171 × 1631 × 71 × 2331
LCM(27710,27727) = 45195010