Least Common Multiple of 65 and 73

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

• Least Common Multiple of 65 and 73 by Prime method
• Least Common Multiple of 65 and 73 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 65 and 73. First we will calculate the prime factors of 65 and 73.

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 73

Prime factors of 73 are 73. Prime factorization of 73 in exponential form is:

73 = 73¹

Now multiplying the highest exponent prime factors to calculate the LCM of 65 and 73.

LCM(65,73) = 5¹×13¹×73¹
LCM(65,73) = 4745

Factors of 65

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

1, 5, 13, 65

Factors of 73

List of positive integer factors of 73 that divides 73 without a remainder.

1, 73

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65 and 73, than apply into the LCM equation.

GCF(65,73) = 1
LCM(65,73) = ( 65 × 73) / 1
LCM(65,73) = 4745 / 1
LCM(65,73) = 4745

(i) The LCM of 73 and 65 is associative

LCM of 65 and 73 = LCM of 73 and 65

1. What is the LCM of 65 and 73?

Answer: LCM of 65 and 73 is 4745.

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 73?

Answer: Factors of 73 are 1, 73. There are 2 integers that are factors of 73. The greatest factor of 73 is 73.

4. How to Find the LCM of 65 and 73?

Answer:

Least Common Multiple of 65 and 73 = 4745

Step 1: Find the prime factorization of 65

65 = 5 x 13

Step 2: Find the prime factorization of 73

73 = 73

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

LCM = 4745 = 5 x 13 x 73

Step 4: Therefore, the least common multiple of 65 and 73 is 4745.