Least Common Multiple of 65 and 2

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

• Least Common Multiple of 65 and 2 by Prime method
• Least Common Multiple of 65 and 2 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 65 and 2. First we will calculate the prime factors of 65 and 2.

Prime Factorization of 65

Prime factors of 65 are 5,13. Prime factorization of 65 in exponential form is:

65 = 5¹×13¹

Prime Factorization of 2

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

2 = 2¹

Now multiplying the highest exponent prime factors to calculate the LCM of 65 and 2.

LCM(65,2) = 2¹×5¹×13¹
LCM(65,2) = 130

Factors of 65

List of positive integer factors of 65 that divides 65 without a remainder.

1, 5, 13, 65

Factors of 2

List of positive integer factors of 2 that divides 2 without a remainder.

1, 2

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65 and 2, than apply into the LCM equation.

GCF(65,2) = 1
LCM(65,2) = ( 65 × 2) / 1
LCM(65,2) = 130 / 1
LCM(65,2) = 130

(i) The LCM of 2 and 65 is associative

LCM of 65 and 2 = LCM of 2 and 65

1. What is the LCM of 65 and 2?

Answer: LCM of 65 and 2 is 130.

2. What are the Factors of 65?

Answer: Factors of 65 are 1, 5, 13, 65. There are 4 integers that are factors of 65. The greatest factor of 65 is 65.

3. What are the Factors of 2?

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

4. How to Find the LCM of 65 and 2?

Answer:

Least Common Multiple of 65 and 2 = 130

Step 1: Find the prime factorization of 65

65 = 5 x 13

Step 2: Find the prime factorization of 2

2 = 2

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

LCM = 130 = 2 x 5 x 13

Step 4: Therefore, the least common multiple of 65 and 2 is 130.