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What is the Least Common Multiple of 17740 and 17748?

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 17740 and 17748 is 78712380.

LCM(17740,17748) = 78712380

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Least Common Multiple of 17740 and 17748 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17740 and 17748, than apply into the LCM equation.

GCF(17740,17748) = 4
LCM(17740,17748) = ( 17740 × 17748) / 4
LCM(17740,17748) = 314849520 / 4
LCM(17740,17748) = 78712380

Least Common Multiple (LCM) of 17740 and 17748 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17740 and 17748. First we will calculate the prime factors of 17740 and 17748.

Prime Factorization of 17740

Prime factors of 17740 are 2, 5, 887. Prime factorization of 17740 in exponential form is:

17740 = 22 × 51 × 8871

Prime Factorization of 17748

Prime factors of 17748 are 2, 3, 17, 29. Prime factorization of 17748 in exponential form is:

17748 = 22 × 32 × 171 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 17740 and 17748.

LCM(17740,17748) = 22 × 51 × 8871 × 32 × 171 × 291
LCM(17740,17748) = 78712380