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What is the Least Common Multiple of 10210 and 10222?

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 10210 and 10222 is 52183310.

LCM(10210,10222) = 52183310

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Least Common Multiple of 10210 and 10222 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10210 and 10222, than apply into the LCM equation.

GCF(10210,10222) = 2
LCM(10210,10222) = ( 10210 × 10222) / 2
LCM(10210,10222) = 104366620 / 2
LCM(10210,10222) = 52183310

Least Common Multiple (LCM) of 10210 and 10222 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10210 and 10222. First we will calculate the prime factors of 10210 and 10222.

Prime Factorization of 10210

Prime factors of 10210 are 2, 5, 1021. Prime factorization of 10210 in exponential form is:

10210 = 21 × 51 × 10211

Prime Factorization of 10222

Prime factors of 10222 are 2, 19, 269. Prime factorization of 10222 in exponential form is:

10222 = 21 × 191 × 2691

Now multiplying the highest exponent prime factors to calculate the LCM of 10210 and 10222.

LCM(10210,10222) = 21 × 51 × 10211 × 191 × 2691
LCM(10210,10222) = 52183310