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What is the Least Common Multiple of 17400 and 17405?

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 17400 and 17405 is 60569400.

LCM(17400,17405) = 60569400

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Least Common Multiple of 17400 and 17405 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17400 and 17405, than apply into the LCM equation.

GCF(17400,17405) = 5
LCM(17400,17405) = ( 17400 × 17405) / 5
LCM(17400,17405) = 302847000 / 5
LCM(17400,17405) = 60569400

Least Common Multiple (LCM) of 17400 and 17405 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17400 and 17405. First we will calculate the prime factors of 17400 and 17405.

Prime Factorization of 17400

Prime factors of 17400 are 2, 3, 5, 29. Prime factorization of 17400 in exponential form is:

17400 = 23 × 31 × 52 × 291

Prime Factorization of 17405

Prime factors of 17405 are 5, 59. Prime factorization of 17405 in exponential form is:

17405 = 51 × 592

Now multiplying the highest exponent prime factors to calculate the LCM of 17400 and 17405.

LCM(17400,17405) = 23 × 31 × 52 × 291 × 592
LCM(17400,17405) = 60569400