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What is the Least Common Multiple of 10742 and 10750?

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 10742 and 10750 is 57738250.

LCM(10742,10750) = 57738250

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Least Common Multiple of 10742 and 10750 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10742 and 10750, than apply into the LCM equation.

GCF(10742,10750) = 2
LCM(10742,10750) = ( 10742 × 10750) / 2
LCM(10742,10750) = 115476500 / 2
LCM(10742,10750) = 57738250

Least Common Multiple (LCM) of 10742 and 10750 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10742 and 10750. First we will calculate the prime factors of 10742 and 10750.

Prime Factorization of 10742

Prime factors of 10742 are 2, 41, 131. Prime factorization of 10742 in exponential form is:

10742 = 21 × 411 × 1311

Prime Factorization of 10750

Prime factors of 10750 are 2, 5, 43. Prime factorization of 10750 in exponential form is:

10750 = 21 × 53 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 10742 and 10750.

LCM(10742,10750) = 21 × 411 × 1311 × 53 × 431
LCM(10742,10750) = 57738250