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What is the Least Common Multiple of 18300 and 18315?

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 18300 and 18315 is 22344300.

LCM(18300,18315) = 22344300

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Least Common Multiple of 18300 and 18315 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18300 and 18315, than apply into the LCM equation.

GCF(18300,18315) = 15
LCM(18300,18315) = ( 18300 × 18315) / 15
LCM(18300,18315) = 335164500 / 15
LCM(18300,18315) = 22344300

Least Common Multiple (LCM) of 18300 and 18315 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 18300 and 18315. First we will calculate the prime factors of 18300 and 18315.

Prime Factorization of 18300

Prime factors of 18300 are 2, 3, 5, 61. Prime factorization of 18300 in exponential form is:

18300 = 22 × 31 × 52 × 611

Prime Factorization of 18315

Prime factors of 18315 are 3, 5, 11, 37. Prime factorization of 18315 in exponential form is:

18315 = 32 × 51 × 111 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 18300 and 18315.

LCM(18300,18315) = 22 × 32 × 52 × 611 × 111 × 371
LCM(18300,18315) = 22344300