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What is the Least Common Multiple of 10174 and 10185?

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 10174 and 10185 is 103622190.

LCM(10174,10185) = 103622190

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Least Common Multiple of 10174 and 10185 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10174 and 10185, than apply into the LCM equation.

GCF(10174,10185) = 1
LCM(10174,10185) = ( 10174 × 10185) / 1
LCM(10174,10185) = 103622190 / 1
LCM(10174,10185) = 103622190

Least Common Multiple (LCM) of 10174 and 10185 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10174 and 10185. First we will calculate the prime factors of 10174 and 10185.

Prime Factorization of 10174

Prime factors of 10174 are 2, 5087. Prime factorization of 10174 in exponential form is:

10174 = 21 × 50871

Prime Factorization of 10185

Prime factors of 10185 are 3, 5, 7, 97. Prime factorization of 10185 in exponential form is:

10185 = 31 × 51 × 71 × 971

Now multiplying the highest exponent prime factors to calculate the LCM of 10174 and 10185.

LCM(10174,10185) = 21 × 50871 × 31 × 51 × 71 × 971
LCM(10174,10185) = 103622190