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What is the Least Common Multiple of 5365 and 5382?

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 5365 and 5382 is 28874430.

LCM(5365,5382) = 28874430

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Least Common Multiple of 5365 and 5382 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5365 and 5382, than apply into the LCM equation.

GCF(5365,5382) = 1
LCM(5365,5382) = ( 5365 × 5382) / 1
LCM(5365,5382) = 28874430 / 1
LCM(5365,5382) = 28874430

Least Common Multiple (LCM) of 5365 and 5382 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5365 and 5382. First we will calculate the prime factors of 5365 and 5382.

Prime Factorization of 5365

Prime factors of 5365 are 5, 29, 37. Prime factorization of 5365 in exponential form is:

5365 = 51 × 291 × 371

Prime Factorization of 5382

Prime factors of 5382 are 2, 3, 13, 23. Prime factorization of 5382 in exponential form is:

5382 = 21 × 32 × 131 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 5365 and 5382.

LCM(5365,5382) = 51 × 291 × 371 × 21 × 32 × 131 × 231
LCM(5365,5382) = 28874430