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What is the Least Common Multiple of 17824 and 17840?

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 17824 and 17840 is 19873760.

LCM(17824,17840) = 19873760

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Least Common Multiple of 17824 and 17840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17824 and 17840, than apply into the LCM equation.

GCF(17824,17840) = 16
LCM(17824,17840) = ( 17824 × 17840) / 16
LCM(17824,17840) = 317980160 / 16
LCM(17824,17840) = 19873760

Least Common Multiple (LCM) of 17824 and 17840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17824 and 17840. First we will calculate the prime factors of 17824 and 17840.

Prime Factorization of 17824

Prime factors of 17824 are 2, 557. Prime factorization of 17824 in exponential form is:

17824 = 25 × 5571

Prime Factorization of 17840

Prime factors of 17840 are 2, 5, 223. Prime factorization of 17840 in exponential form is:

17840 = 24 × 51 × 2231

Now multiplying the highest exponent prime factors to calculate the LCM of 17824 and 17840.

LCM(17824,17840) = 25 × 5571 × 51 × 2231
LCM(17824,17840) = 19873760