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What is the Least Common Multiple of 17724 and 17731?

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 17724 and 17731 is 44894892.

LCM(17724,17731) = 44894892

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Least Common Multiple of 17724 and 17731 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17724 and 17731, than apply into the LCM equation.

GCF(17724,17731) = 7
LCM(17724,17731) = ( 17724 × 17731) / 7
LCM(17724,17731) = 314264244 / 7
LCM(17724,17731) = 44894892

Least Common Multiple (LCM) of 17724 and 17731 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17724 and 17731. First we will calculate the prime factors of 17724 and 17731.

Prime Factorization of 17724

Prime factors of 17724 are 2, 3, 7, 211. Prime factorization of 17724 in exponential form is:

17724 = 22 × 31 × 71 × 2111

Prime Factorization of 17731

Prime factors of 17731 are 7, 17, 149. Prime factorization of 17731 in exponential form is:

17731 = 71 × 171 × 1491

Now multiplying the highest exponent prime factors to calculate the LCM of 17724 and 17731.

LCM(17724,17731) = 22 × 31 × 71 × 2111 × 171 × 1491
LCM(17724,17731) = 44894892