Least Common Multiple of 4 and 17

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

• Least Common Multiple of 4 and 17 by Prime method
• Least Common Multiple of 4 and 17 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 4 and 17. First we will calculate the prime factors of 4 and 17.

Prime Factorization of 4

Prime factors of 4 are 2. Prime factorization of 4 in exponential form is:

4 = 2²

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 4 and 17.

LCM(4,17) = 2²×17¹
LCM(4,17) = 68

Factors of 4

List of positive integer factors of 4 that divides 4 without a remainder.

1, 2, 4

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 4 and 17, than apply into the LCM equation.

GCF(4,17) = 1
LCM(4,17) = ( 4 × 17) / 1
LCM(4,17) = 68 / 1
LCM(4,17) = 68

(i) The LCM of 17 and 4 is associative

LCM of 4 and 17 = LCM of 17 and 4

1. What is the LCM of 4 and 17?

Answer: LCM of 4 and 17 is 68.

2. What are the Factors of 4?

Answer: Factors of 4 are 1, 2, 4. There are 3 integers that are factors of 4. The greatest factor of 4 is 4.

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 4 and 17?

Answer:

Least Common Multiple of 4 and 17 = 68

Step 1: Find the prime factorization of 4

4 = 2 x 2

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 = 68 = 2 x 2 x 17

Step 4: Therefore, the least common multiple of 4 and 17 is 68.