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What is the Least Common Multiple of 27700 and 27710?

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 27700 and 27710 is 76756700.

LCM(27700,27710) = 76756700

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Least Common Multiple of 27700 and 27710 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27700 and 27710, than apply into the LCM equation.

GCF(27700,27710) = 10
LCM(27700,27710) = ( 27700 × 27710) / 10
LCM(27700,27710) = 767567000 / 10
LCM(27700,27710) = 76756700

Least Common Multiple (LCM) of 27700 and 27710 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27700 and 27710. First we will calculate the prime factors of 27700 and 27710.

Prime Factorization of 27700

Prime factors of 27700 are 2, 5, 277. Prime factorization of 27700 in exponential form is:

27700 = 22 × 52 × 2771

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

Now multiplying the highest exponent prime factors to calculate the LCM of 27700 and 27710.

LCM(27700,27710) = 22 × 52 × 2771 × 171 × 1631
LCM(27700,27710) = 76756700