Least Common Multiple of 17231 and 17238

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

• Least Common Multiple of 17231 and 17238 by Prime method
• Least Common Multiple of 17231 and 17238 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 17231 and 17238. First we will calculate the prime factors of 17231 and 17238.

Prime Factorization of 17231

Prime factors of 17231 are 17231. Prime factorization of 17231 in exponential form is:

17231 = 17231¹

Prime Factorization of 17238

Prime factors of 17238 are 2, 3, 13,17. Prime factorization of 17238 in exponential form is:

17238 = 2¹×3¹×13²×17¹

Now multiplying the highest exponent prime factors to calculate the LCM of 17231 and 17238.

LCM(17231,17238) = 2¹×3¹×13²×17¹×17231¹
LCM(17231,17238) = 297027978

Factors of 17231

List of positive integer factors of 17231 that divides 17231 without a remainder.

1, 17231

Factors of 17238

List of positive integer factors of 17238 that divides 17238 without a remainder.

1, 2, 3, 6, 13, 17, 26, 34, 39, 51, 78, 102, 169, 221, 338, 442, 507, 663, 1014, 1326, 2873, 5746, 8619, 17238

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17231 and 17238, than apply into the LCM equation.

GCF(17231,17238) = 1
LCM(17231,17238) = ( 17231 × 17238) / 1
LCM(17231,17238) = 297027978 / 1
LCM(17231,17238) = 297027978

(i) The LCM of 17238 and 17231 is associative

LCM of 17231 and 17238 = LCM of 17238 and 17231

1. What is the LCM of 17231 and 17238?

Answer: LCM of 17231 and 17238 is 297027978.

2. What are the Factors of 17231?

Answer: Factors of 17231 are 1, 17231. There are 2 integers that are factors of 17231. The greatest factor of 17231 is 17231.

3. What are the Factors of 17238?

Answer: Factors of 17238 are 1, 2, 3, 6, 13, 17, 26, 34, 39, 51, 78, 102, 169, 221, 338, 442, 507, 663, 1014, 1326, 2873, 5746, 8619, 17238. There are 24 integers that are factors of 17238. The greatest factor of 17238 is 17238.

4. How to Find the LCM of 17231 and 17238?

Answer:

Least Common Multiple of 17231 and 17238 = 297027978

Step 1: Find the prime factorization of 17231

17231 = 17231

Step 2: Find the prime factorization of 17238

17238 = 2 x 3 x 13 x 13 x 17

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

LCM = 297027978 = 2 x 3 x 13 x 13 x 17 x 17231

Step 4: Therefore, the least common multiple of 17231 and 17238 is 297027978.