Least Common Multiple of 17 and 18

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

• Least Common Multiple of 17 and 18 by Prime method
• Least Common Multiple of 17 and 18 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 17 and 18. First we will calculate the prime factors of 17 and 18.

Prime Factorization of 17

Prime factors of 17 are 17. Prime factorization of 17 in exponential form is:

17 = 17¹

Prime Factorization of 18

Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:

18 = 2¹×3²

Now multiplying the highest exponent prime factors to calculate the LCM of 17 and 18.

LCM(17,18) = 2¹×3²×17¹
LCM(17,18) = 306

Factors of 17

List of positive integer factors of 17 that divides 17 without a remainder.

1, 17

Factors of 18

List of positive integer factors of 18 that divides 18 without a remainder.

1, 2, 3, 6, 9, 18

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17 and 18, than apply into the LCM equation.

GCF(17,18) = 1
LCM(17,18) = ( 17 × 18) / 1
LCM(17,18) = 306 / 1
LCM(17,18) = 306

(i) The LCM of 18 and 17 is associative

LCM of 17 and 18 = LCM of 18 and 17

1. What is the LCM of 17 and 18?

Answer: LCM of 17 and 18 is 306.

2. What are the Factors of 17?

Answer: Factors of 17 are 1, 17. There are 2 integers that are factors of 17. The greatest factor of 17 is 17.

3. What are the Factors of 18?

Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.

4. How to Find the LCM of 17 and 18?

Answer:

Least Common Multiple of 17 and 18 = 306

Step 1: Find the prime factorization of 17

17 = 17

Step 2: Find the prime factorization of 18

18 = 2 x 3 x 3

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

LCM = 306 = 2 x 3 x 3 x 17

Step 4: Therefore, the least common multiple of 17 and 18 is 306.