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What is the Least Common Multiple of 54735 and 54744?

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 54735 and 54744 is 998804280.

LCM(54735,54744) = 998804280

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Least Common Multiple of 54735 and 54744 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54735 and 54744, than apply into the LCM equation.

GCF(54735,54744) = 3
LCM(54735,54744) = ( 54735 × 54744) / 3
LCM(54735,54744) = 2996412840 / 3
LCM(54735,54744) = 998804280

Least Common Multiple (LCM) of 54735 and 54744 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54735 and 54744. First we will calculate the prime factors of 54735 and 54744.

Prime Factorization of 54735

Prime factors of 54735 are 3, 5, 41, 89. Prime factorization of 54735 in exponential form is:

54735 = 31 × 51 × 411 × 891

Prime Factorization of 54744

Prime factors of 54744 are 2, 3, 2281. Prime factorization of 54744 in exponential form is:

54744 = 23 × 31 × 22811

Now multiplying the highest exponent prime factors to calculate the LCM of 54735 and 54744.

LCM(54735,54744) = 31 × 51 × 411 × 891 × 23 × 22811
LCM(54735,54744) = 998804280