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What is the Least Common Multiple of 17730 and 17746?

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 17730 and 17746 is 157318290.

LCM(17730,17746) = 157318290

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Least Common Multiple of 17730 and 17746 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17730 and 17746, than apply into the LCM equation.

GCF(17730,17746) = 2
LCM(17730,17746) = ( 17730 × 17746) / 2
LCM(17730,17746) = 314636580 / 2
LCM(17730,17746) = 157318290

Least Common Multiple (LCM) of 17730 and 17746 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17730 and 17746. First we will calculate the prime factors of 17730 and 17746.

Prime Factorization of 17730

Prime factors of 17730 are 2, 3, 5, 197. Prime factorization of 17730 in exponential form is:

17730 = 21 × 32 × 51 × 1971

Prime Factorization of 17746

Prime factors of 17746 are 2, 19, 467. Prime factorization of 17746 in exponential form is:

17746 = 21 × 191 × 4671

Now multiplying the highest exponent prime factors to calculate the LCM of 17730 and 17746.

LCM(17730,17746) = 21 × 32 × 51 × 1971 × 191 × 4671
LCM(17730,17746) = 157318290