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What is the Least Common Multiple of 12282 and 12300?

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 12282 and 12300 is 25178100.

LCM(12282,12300) = 25178100

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Least Common Multiple of 12282 and 12300 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12282 and 12300, than apply into the LCM equation.

GCF(12282,12300) = 6
LCM(12282,12300) = ( 12282 × 12300) / 6
LCM(12282,12300) = 151068600 / 6
LCM(12282,12300) = 25178100

Least Common Multiple (LCM) of 12282 and 12300 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12282 and 12300. First we will calculate the prime factors of 12282 and 12300.

Prime Factorization of 12282

Prime factors of 12282 are 2, 3, 23, 89. Prime factorization of 12282 in exponential form is:

12282 = 21 × 31 × 231 × 891

Prime Factorization of 12300

Prime factors of 12300 are 2, 3, 5, 41. Prime factorization of 12300 in exponential form is:

12300 = 22 × 31 × 52 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 12282 and 12300.

LCM(12282,12300) = 22 × 31 × 231 × 891 × 52 × 411
LCM(12282,12300) = 25178100