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What is the Least Common Multiple of 10730 and 10738?

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 10730 and 10738 is 57609370.

LCM(10730,10738) = 57609370

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Least Common Multiple of 10730 and 10738 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10730 and 10738, than apply into the LCM equation.

GCF(10730,10738) = 2
LCM(10730,10738) = ( 10730 × 10738) / 2
LCM(10730,10738) = 115218740 / 2
LCM(10730,10738) = 57609370

Least Common Multiple (LCM) of 10730 and 10738 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10730 and 10738. First we will calculate the prime factors of 10730 and 10738.

Prime Factorization of 10730

Prime factors of 10730 are 2, 5, 29, 37. Prime factorization of 10730 in exponential form is:

10730 = 21 × 51 × 291 × 371

Prime Factorization of 10738

Prime factors of 10738 are 2, 7, 13, 59. Prime factorization of 10738 in exponential form is:

10738 = 21 × 71 × 131 × 591

Now multiplying the highest exponent prime factors to calculate the LCM of 10730 and 10738.

LCM(10730,10738) = 21 × 51 × 291 × 371 × 71 × 131 × 591
LCM(10730,10738) = 57609370