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What is the Least Common Multiple of 27706 and 27720?

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 27706 and 27720 is 54857880.

LCM(27706,27720) = 54857880

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Least Common Multiple of 27706 and 27720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27706 and 27720, than apply into the LCM equation.

GCF(27706,27720) = 14
LCM(27706,27720) = ( 27706 × 27720) / 14
LCM(27706,27720) = 768010320 / 14
LCM(27706,27720) = 54857880

Least Common Multiple (LCM) of 27706 and 27720 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27706 and 27720. First we will calculate the prime factors of 27706 and 27720.

Prime Factorization of 27706

Prime factors of 27706 are 2, 7, 1979. Prime factorization of 27706 in exponential form is:

27706 = 21 × 71 × 19791

Prime Factorization of 27720

Prime factors of 27720 are 2, 3, 5, 7, 11. Prime factorization of 27720 in exponential form is:

27720 = 23 × 32 × 51 × 71 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 27706 and 27720.

LCM(27706,27720) = 23 × 71 × 19791 × 32 × 51 × 111
LCM(27706,27720) = 54857880