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What is the Least Common Multiple of 54280 and 54296?

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 54280 and 54296 is 368398360.

LCM(54280,54296) = 368398360

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Least Common Multiple of 54280 and 54296 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54280 and 54296, than apply into the LCM equation.

GCF(54280,54296) = 8
LCM(54280,54296) = ( 54280 × 54296) / 8
LCM(54280,54296) = 2947186880 / 8
LCM(54280,54296) = 368398360

Least Common Multiple (LCM) of 54280 and 54296 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54280 and 54296. First we will calculate the prime factors of 54280 and 54296.

Prime Factorization of 54280

Prime factors of 54280 are 2, 5, 23, 59. Prime factorization of 54280 in exponential form is:

54280 = 23 × 51 × 231 × 591

Prime Factorization of 54296

Prime factors of 54296 are 2, 11, 617. Prime factorization of 54296 in exponential form is:

54296 = 23 × 111 × 6171

Now multiplying the highest exponent prime factors to calculate the LCM of 54280 and 54296.

LCM(54280,54296) = 23 × 51 × 231 × 591 × 111 × 6171
LCM(54280,54296) = 368398360