Least Common Multiple of 17 and 21

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

• Least Common Multiple of 17 and 21 by Prime method
• Least Common Multiple of 17 and 21 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 17 and 21. First we will calculate the prime factors of 17 and 21.

Prime Factorization of 17

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

17 = 17¹

Prime Factorization of 21

Prime factors of 21 are 3,7. Prime factorization of 21 in exponential form is:

21 = 3¹×7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 17 and 21.

LCM(17,21) = 3¹×7¹×17¹
LCM(17,21) = 357

Factors of 17

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

1, 17

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1, 3, 7, 21

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17 and 21, than apply into the LCM equation.

GCF(17,21) = 1
LCM(17,21) = ( 17 × 21) / 1
LCM(17,21) = 357 / 1
LCM(17,21) = 357

(i) The LCM of 21 and 17 is associative

LCM of 17 and 21 = LCM of 21 and 17

1. What is the LCM of 17 and 21?

Answer: LCM of 17 and 21 is 357.

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 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

4. How to Find the LCM of 17 and 21?

Answer:

Least Common Multiple of 17 and 21 = 357

Step 1: Find the prime factorization of 17

17 = 17

Step 2: Find the prime factorization of 21

21 = 3 x 7

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

LCM = 357 = 3 x 7 x 17

Step 4: Therefore, the least common multiple of 17 and 21 is 357.