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What is the Least Common Multiple of 10203 and 10212?

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 10203 and 10212 is 34731012.

LCM(10203,10212) = 34731012

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Least Common Multiple of 10203 and 10212 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10203 and 10212, than apply into the LCM equation.

GCF(10203,10212) = 3
LCM(10203,10212) = ( 10203 × 10212) / 3
LCM(10203,10212) = 104193036 / 3
LCM(10203,10212) = 34731012

Least Common Multiple (LCM) of 10203 and 10212 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10203 and 10212. First we will calculate the prime factors of 10203 and 10212.

Prime Factorization of 10203

Prime factors of 10203 are 3, 19, 179. Prime factorization of 10203 in exponential form is:

10203 = 31 × 191 × 1791

Prime Factorization of 10212

Prime factors of 10212 are 2, 3, 23, 37. Prime factorization of 10212 in exponential form is:

10212 = 22 × 31 × 231 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 10203 and 10212.

LCM(10203,10212) = 31 × 191 × 1791 × 22 × 231 × 371
LCM(10203,10212) = 34731012