Least Common Multiple of 9 and 26

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

• Least Common Multiple of 9 and 26 by Prime method
• Least Common Multiple of 9 and 26 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 26. First we will calculate the prime factors of 9 and 26.

Prime Factorization of 9

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 3²

Prime Factorization of 26

Prime factors of 26 are 2,13. Prime factorization of 26 in exponential form is:

26 = 2¹×13¹

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 26.

LCM(9,26) = 2¹×3²×13¹
LCM(9,26) = 234

Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1, 3, 9

Factors of 26

List of positive integer factors of 26 that divides 26 without a remainder.

1, 2, 13, 26

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 26, than apply into the LCM equation.

GCF(9,26) = 1
LCM(9,26) = ( 9 × 26) / 1
LCM(9,26) = 234 / 1
LCM(9,26) = 234

(i) The LCM of 26 and 9 is associative

LCM of 9 and 26 = LCM of 26 and 9

1. What is the LCM of 9 and 26?

Answer: LCM of 9 and 26 is 234.

2. What are the Factors of 9?

Answer: Factors of 9 are 1, 3, 9. There are 3 integers that are factors of 9. The greatest factor of 9 is 9.

3. What are the Factors of 26?

Answer: Factors of 26 are 1, 2, 13, 26. There are 4 integers that are factors of 26. The greatest factor of 26 is 26.

4. How to Find the LCM of 9 and 26?

Answer:

Least Common Multiple of 9 and 26 = 234

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 26

26 = 2 x 13

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

LCM = 234 = 2 x 3 x 3 x 13

Step 4: Therefore, the least common multiple of 9 and 26 is 234.