Least Common Multiple of 3 and 17

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

• Least Common Multiple of 3 and 17 by Prime method
• Least Common Multiple of 3 and 17 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 17. First we will calculate the prime factors of 3 and 17.

Prime Factorization of 3

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

3 = 3¹

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 3 and 17.

LCM(3,17) = 3¹×17¹
LCM(3,17) = 51

Factors of 3

List of positive integer factors of 3 that divides 3 without a remainder.

1, 3

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 3 and 17, than apply into the LCM equation.

GCF(3,17) = 1
LCM(3,17) = ( 3 × 17) / 1
LCM(3,17) = 51 / 1
LCM(3,17) = 51

(i) The LCM of 17 and 3 is associative

LCM of 3 and 17 = LCM of 17 and 3

1. What is the LCM of 3 and 17?

Answer: LCM of 3 and 17 is 51.

2. What are the Factors of 3?

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

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 3 and 17?

Answer:

Least Common Multiple of 3 and 17 = 51

Step 1: Find the prime factorization of 3

3 = 3

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 = 51 = 3 x 17

Step 4: Therefore, the least common multiple of 3 and 17 is 51.