Least Common Multiple of 14 and 17

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

• Least Common Multiple of 14 and 17 by Prime method
• Least Common Multiple of 14 and 17 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 14 and 17. First we will calculate the prime factors of 14 and 17.

Prime Factorization of 14

Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:

14 = 2¹×7¹

Prime Factorization of 17

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

17 = 17¹

Now multiplying the highest exponent prime factors to calculate the LCM of 14 and 17.

LCM(14,17) = 2¹×7¹×17¹
LCM(14,17) = 238

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1, 2, 7, 14

Factors of 17

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

1, 17

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14 and 17, than apply into the LCM equation.

GCF(14,17) = 1
LCM(14,17) = ( 14 × 17) / 1
LCM(14,17) = 238 / 1
LCM(14,17) = 238

(i) The LCM of 17 and 14 is associative

LCM of 14 and 17 = LCM of 17 and 14

1. What is the LCM of 14 and 17?

Answer: LCM of 14 and 17 is 238.

2. What are the Factors of 14?

Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.

3. 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.

4. How to Find the LCM of 14 and 17?

Answer:

Least Common Multiple of 14 and 17 = 238

Step 1: Find the prime factorization of 14

14 = 2 x 7

Step 2: Find the prime factorization of 17

17 = 17

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

LCM = 238 = 2 x 7 x 17

Step 4: Therefore, the least common multiple of 14 and 17 is 238.