Least Common Multiple of 65 and 71

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

• Least Common Multiple of 65 and 71 by Prime method
• Least Common Multiple of 65 and 71 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 65 and 71. First we will calculate the prime factors of 65 and 71.

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 71

Prime factors of 71 are 71. Prime factorization of 71 in exponential form is:

71 = 71¹

Now multiplying the highest exponent prime factors to calculate the LCM of 65 and 71.

LCM(65,71) = 5¹×13¹×71¹
LCM(65,71) = 4615

Factors of 65

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

1, 5, 13, 65

Factors of 71

List of positive integer factors of 71 that divides 71 without a remainder.

1, 71

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65 and 71, than apply into the LCM equation.

GCF(65,71) = 1
LCM(65,71) = ( 65 × 71) / 1
LCM(65,71) = 4615 / 1
LCM(65,71) = 4615

(i) The LCM of 71 and 65 is associative

LCM of 65 and 71 = LCM of 71 and 65

1. What is the LCM of 65 and 71?

Answer: LCM of 65 and 71 is 4615.

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 71?

Answer: Factors of 71 are 1, 71. There are 2 integers that are factors of 71. The greatest factor of 71 is 71.

4. How to Find the LCM of 65 and 71?

Answer:

Least Common Multiple of 65 and 71 = 4615

Step 1: Find the prime factorization of 65

65 = 5 x 13

Step 2: Find the prime factorization of 71

71 = 71

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

LCM = 4615 = 5 x 13 x 71

Step 4: Therefore, the least common multiple of 65 and 71 is 4615.