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What is the Least Common Multiple of 17990 and 18008?

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 17990 and 18008 is 161981960.

LCM(17990,18008) = 161981960

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Least Common Multiple of 17990 and 18008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17990 and 18008, than apply into the LCM equation.

GCF(17990,18008) = 2
LCM(17990,18008) = ( 17990 × 18008) / 2
LCM(17990,18008) = 323963920 / 2
LCM(17990,18008) = 161981960

Least Common Multiple (LCM) of 17990 and 18008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17990 and 18008. First we will calculate the prime factors of 17990 and 18008.

Prime Factorization of 17990

Prime factors of 17990 are 2, 5, 7, 257. Prime factorization of 17990 in exponential form is:

17990 = 21 × 51 × 71 × 2571

Prime Factorization of 18008

Prime factors of 18008 are 2, 2251. Prime factorization of 18008 in exponential form is:

18008 = 23 × 22511

Now multiplying the highest exponent prime factors to calculate the LCM of 17990 and 18008.

LCM(17990,18008) = 23 × 51 × 71 × 2571 × 22511
LCM(17990,18008) = 161981960