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What is the Least Common Multiple of 10178 and 10188?

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 10178 and 10188 is 51846732.

LCM(10178,10188) = 51846732

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Least Common Multiple of 10178 and 10188 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10178 and 10188, than apply into the LCM equation.

GCF(10178,10188) = 2
LCM(10178,10188) = ( 10178 × 10188) / 2
LCM(10178,10188) = 103693464 / 2
LCM(10178,10188) = 51846732

Least Common Multiple (LCM) of 10178 and 10188 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10178 and 10188. First we will calculate the prime factors of 10178 and 10188.

Prime Factorization of 10178

Prime factors of 10178 are 2, 7, 727. Prime factorization of 10178 in exponential form is:

10178 = 21 × 71 × 7271

Prime Factorization of 10188

Prime factors of 10188 are 2, 3, 283. Prime factorization of 10188 in exponential form is:

10188 = 22 × 32 × 2831

Now multiplying the highest exponent prime factors to calculate the LCM of 10178 and 10188.

LCM(10178,10188) = 22 × 71 × 7271 × 32 × 2831
LCM(10178,10188) = 51846732