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What is the Least Common Multiple of 17673 and 17689?

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 17673 and 17689 is 312617697.

LCM(17673,17689) = 312617697

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Least Common Multiple of 17673 and 17689 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17673 and 17689, than apply into the LCM equation.

GCF(17673,17689) = 1
LCM(17673,17689) = ( 17673 × 17689) / 1
LCM(17673,17689) = 312617697 / 1
LCM(17673,17689) = 312617697

Least Common Multiple (LCM) of 17673 and 17689 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17673 and 17689. First we will calculate the prime factors of 17673 and 17689.

Prime Factorization of 17673

Prime factors of 17673 are 3, 43, 137. Prime factorization of 17673 in exponential form is:

17673 = 31 × 431 × 1371

Prime Factorization of 17689

Prime factors of 17689 are 7, 19. Prime factorization of 17689 in exponential form is:

17689 = 72 × 192

Now multiplying the highest exponent prime factors to calculate the LCM of 17673 and 17689.

LCM(17673,17689) = 31 × 431 × 1371 × 72 × 192
LCM(17673,17689) = 312617697