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What is the Least Common Multiple of 17748 and 17760?

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 17748 and 17760 is 26267040.

LCM(17748,17760) = 26267040

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Least Common Multiple of 17748 and 17760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17748 and 17760, than apply into the LCM equation.

GCF(17748,17760) = 12
LCM(17748,17760) = ( 17748 × 17760) / 12
LCM(17748,17760) = 315204480 / 12
LCM(17748,17760) = 26267040

Least Common Multiple (LCM) of 17748 and 17760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17748 and 17760. First we will calculate the prime factors of 17748 and 17760.

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

Prime Factorization of 17760

Prime factors of 17760 are 2, 3, 5, 37. Prime factorization of 17760 in exponential form is:

17760 = 25 × 31 × 51 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 17748 and 17760.

LCM(17748,17760) = 25 × 32 × 171 × 291 × 51 × 371
LCM(17748,17760) = 26267040