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What is the Least Common Multiple of 10230 and 10239?

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 10230 and 10239 is 34914990.

LCM(10230,10239) = 34914990

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Least Common Multiple of 10230 and 10239 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10230 and 10239, than apply into the LCM equation.

GCF(10230,10239) = 3
LCM(10230,10239) = ( 10230 × 10239) / 3
LCM(10230,10239) = 104744970 / 3
LCM(10230,10239) = 34914990

Least Common Multiple (LCM) of 10230 and 10239 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10230 and 10239. First we will calculate the prime factors of 10230 and 10239.

Prime Factorization of 10230

Prime factors of 10230 are 2, 3, 5, 11, 31. Prime factorization of 10230 in exponential form is:

10230 = 21 × 31 × 51 × 111 × 311

Prime Factorization of 10239

Prime factors of 10239 are 3, 3413. Prime factorization of 10239 in exponential form is:

10239 = 31 × 34131

Now multiplying the highest exponent prime factors to calculate the LCM of 10230 and 10239.

LCM(10230,10239) = 21 × 31 × 51 × 111 × 311 × 34131
LCM(10230,10239) = 34914990