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What is the Least Common Multiple of 10219 and 10230?

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 10219 and 10230 is 9503670.

LCM(10219,10230) = 9503670

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Least Common Multiple of 10219 and 10230 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10219 and 10230, than apply into the LCM equation.

GCF(10219,10230) = 11
LCM(10219,10230) = ( 10219 × 10230) / 11
LCM(10219,10230) = 104540370 / 11
LCM(10219,10230) = 9503670

Least Common Multiple (LCM) of 10219 and 10230 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10219 and 10230. First we will calculate the prime factors of 10219 and 10230.

Prime Factorization of 10219

Prime factors of 10219 are 11, 929. Prime factorization of 10219 in exponential form is:

10219 = 111 × 9291

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

Now multiplying the highest exponent prime factors to calculate the LCM of 10219 and 10230.

LCM(10219,10230) = 111 × 9291 × 21 × 31 × 51 × 311
LCM(10219,10230) = 9503670