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What is the Least Common Multiple of 27744 and 27761?

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 27744 and 27761 is 45305952.

LCM(27744,27761) = 45305952

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Least Common Multiple of 27744 and 27761 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27744 and 27761, than apply into the LCM equation.

GCF(27744,27761) = 17
LCM(27744,27761) = ( 27744 × 27761) / 17
LCM(27744,27761) = 770201184 / 17
LCM(27744,27761) = 45305952

Least Common Multiple (LCM) of 27744 and 27761 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27744 and 27761. First we will calculate the prime factors of 27744 and 27761.

Prime Factorization of 27744

Prime factors of 27744 are 2, 3, 17. Prime factorization of 27744 in exponential form is:

27744 = 25 × 31 × 172

Prime Factorization of 27761

Prime factors of 27761 are 17, 23, 71. Prime factorization of 27761 in exponential form is:

27761 = 171 × 231 × 711

Now multiplying the highest exponent prime factors to calculate the LCM of 27744 and 27761.

LCM(27744,27761) = 25 × 31 × 172 × 231 × 711
LCM(27744,27761) = 45305952