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What is the Least Common Multiple of 10206 and 10220?

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 10206 and 10220 is 7450380.

LCM(10206,10220) = 7450380

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Least Common Multiple of 10206 and 10220 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10206 and 10220, than apply into the LCM equation.

GCF(10206,10220) = 14
LCM(10206,10220) = ( 10206 × 10220) / 14
LCM(10206,10220) = 104305320 / 14
LCM(10206,10220) = 7450380

Least Common Multiple (LCM) of 10206 and 10220 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10206 and 10220. First we will calculate the prime factors of 10206 and 10220.

Prime Factorization of 10206

Prime factors of 10206 are 2, 3, 7. Prime factorization of 10206 in exponential form is:

10206 = 21 × 36 × 71

Prime Factorization of 10220

Prime factors of 10220 are 2, 5, 7, 73. Prime factorization of 10220 in exponential form is:

10220 = 22 × 51 × 71 × 731

Now multiplying the highest exponent prime factors to calculate the LCM of 10206 and 10220.

LCM(10206,10220) = 22 × 36 × 71 × 51 × 731
LCM(10206,10220) = 7450380