Least Common Multiple of 61 and 65

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

• Least Common Multiple of 61 and 65 by Prime method
• Least Common Multiple of 61 and 65 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 61 and 65. First we will calculate the prime factors of 61 and 65.

Prime Factorization of 61

Prime factors of 61 are 61. Prime factorization of 61 in exponential form is:

61 = 61¹

Prime Factorization of 65

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

65 = 5¹×13¹

Now multiplying the highest exponent prime factors to calculate the LCM of 61 and 65.

LCM(61,65) = 5¹×13¹×61¹
LCM(61,65) = 3965

Factors of 61

List of positive integer factors of 61 that divides 61 without a remainder.

1, 61

Factors of 65

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

1, 5, 13, 65

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 61 and 65, than apply into the LCM equation.

GCF(61,65) = 1
LCM(61,65) = ( 61 × 65) / 1
LCM(61,65) = 3965 / 1
LCM(61,65) = 3965

(i) The LCM of 65 and 61 is associative

LCM of 61 and 65 = LCM of 65 and 61

1. What is the LCM of 61 and 65?

Answer: LCM of 61 and 65 is 3965.

2. What are the Factors of 61?

Answer: Factors of 61 are 1, 61. There are 2 integers that are factors of 61. The greatest factor of 61 is 61.

3. 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.

4. How to Find the LCM of 61 and 65?

Answer:

Least Common Multiple of 61 and 65 = 3965

Step 1: Find the prime factorization of 61

61 = 61

Step 2: Find the prime factorization of 65

65 = 5 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 = 3965 = 5 x 13 x 61

Step 4: Therefore, the least common multiple of 61 and 65 is 3965.