Least Common Multiple of 17 and 22

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

• Least Common Multiple of 17 and 22 by Prime method
• Least Common Multiple of 17 and 22 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 17 and 22. First we will calculate the prime factors of 17 and 22.

Prime Factorization of 17

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

17 = 17¹

Prime Factorization of 22

Prime factors of 22 are 2,11. Prime factorization of 22 in exponential form is:

22 = 2¹×11¹

Now multiplying the highest exponent prime factors to calculate the LCM of 17 and 22.

LCM(17,22) = 2¹×11¹×17¹
LCM(17,22) = 374

Factors of 17

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

1, 17

Factors of 22

List of positive integer factors of 22 that divides 22 without a remainder.

1, 2, 11, 22

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17 and 22, than apply into the LCM equation.

GCF(17,22) = 1
LCM(17,22) = ( 17 × 22) / 1
LCM(17,22) = 374 / 1
LCM(17,22) = 374

(i) The LCM of 22 and 17 is associative

LCM of 17 and 22 = LCM of 22 and 17

1. What is the LCM of 17 and 22?

Answer: LCM of 17 and 22 is 374.

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 22?

Answer: Factors of 22 are 1, 2, 11, 22. There are 4 integers that are factors of 22. The greatest factor of 22 is 22.

4. How to Find the LCM of 17 and 22?

Answer:

Least Common Multiple of 17 and 22 = 374

Step 1: Find the prime factorization of 17

17 = 17

Step 2: Find the prime factorization of 22

22 = 2 x 11

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

LCM = 374 = 2 x 11 x 17

Step 4: Therefore, the least common multiple of 17 and 22 is 374.