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What is the Least Common Multiple of 17224 and 17228?

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 17224 and 17228 is 74183768.

LCM(17224,17228) = 74183768

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Least Common Multiple of 17224 and 17228 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17224 and 17228, than apply into the LCM equation.

GCF(17224,17228) = 4
LCM(17224,17228) = ( 17224 × 17228) / 4
LCM(17224,17228) = 296735072 / 4
LCM(17224,17228) = 74183768

Least Common Multiple (LCM) of 17224 and 17228 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17224 and 17228. First we will calculate the prime factors of 17224 and 17228.

Prime Factorization of 17224

Prime factors of 17224 are 2, 2153. Prime factorization of 17224 in exponential form is:

17224 = 23 × 21531

Prime Factorization of 17228

Prime factors of 17228 are 2, 59, 73. Prime factorization of 17228 in exponential form is:

17228 = 22 × 591 × 731

Now multiplying the highest exponent prime factors to calculate the LCM of 17224 and 17228.

LCM(17224,17228) = 23 × 21531 × 591 × 731
LCM(17224,17228) = 74183768