Least Common Multiple of 17204 and 17209

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

• Least Common Multiple of 17204 and 17209 by Prime method
• Least Common Multiple of 17204 and 17209 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 17204 and 17209. First we will calculate the prime factors of 17204 and 17209.

Prime Factorization of 17204

Prime factors of 17204 are 2, 11, 17,23. Prime factorization of 17204 in exponential form is:

17204 = 2²×11¹×17¹×23¹

Prime Factorization of 17209

Prime factors of 17209 are 17209. Prime factorization of 17209 in exponential form is:

17209 = 17209¹

Now multiplying the highest exponent prime factors to calculate the LCM of 17204 and 17209.

LCM(17204,17209) = 2²×11¹×17¹×23¹×17209¹
LCM(17204,17209) = 296063636

Factors of 17204

List of positive integer factors of 17204 that divides 17204 without a remainder.

1, 2, 4, 11, 17, 22, 23, 34, 44, 46, 68, 92, 187, 253, 374, 391, 506, 748, 782, 1012, 1564, 4301, 8602, 17204

Factors of 17209

List of positive integer factors of 17209 that divides 17209 without a remainder.

1, 17209

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17204 and 17209, than apply into the LCM equation.

GCF(17204,17209) = 1
LCM(17204,17209) = ( 17204 × 17209) / 1
LCM(17204,17209) = 296063636 / 1
LCM(17204,17209) = 296063636

(i) The LCM of 17209 and 17204 is associative

LCM of 17204 and 17209 = LCM of 17209 and 17204

1. What is the LCM of 17204 and 17209?

Answer: LCM of 17204 and 17209 is 296063636.

2. What are the Factors of 17204?

Answer: Factors of 17204 are 1, 2, 4, 11, 17, 22, 23, 34, 44, 46, 68, 92, 187, 253, 374, 391, 506, 748, 782, 1012, 1564, 4301, 8602, 17204. There are 24 integers that are factors of 17204. The greatest factor of 17204 is 17204.

3. What are the Factors of 17209?

Answer: Factors of 17209 are 1, 17209. There are 2 integers that are factors of 17209. The greatest factor of 17209 is 17209.

4. How to Find the LCM of 17204 and 17209?

Answer:

Least Common Multiple of 17204 and 17209 = 296063636

Step 1: Find the prime factorization of 17204

17204 = 2 x 2 x 11 x 17 x 23

Step 2: Find the prime factorization of 17209

17209 = 17209

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 296063636 = 2 x 2 x 11 x 17 x 23 x 17209

Step 4: Therefore, the least common multiple of 17204 and 17209 is 296063636.