Least Common Multiple of 59 and 65

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

• Least Common Multiple of 59 and 65 by Prime method
• Least Common Multiple of 59 and 65 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 59 and 65. First we will calculate the prime factors of 59 and 65.

Prime Factorization of 59

Prime factors of 59 are 59. Prime factorization of 59 in exponential form is:

59 = 59¹

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 59 and 65.

LCM(59,65) = 5¹×13¹×59¹
LCM(59,65) = 3835

Factors of 59

List of positive integer factors of 59 that divides 59 without a remainder.

1, 59

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 59 and 65, than apply into the LCM equation.

GCF(59,65) = 1
LCM(59,65) = ( 59 × 65) / 1
LCM(59,65) = 3835 / 1
LCM(59,65) = 3835

(i) The LCM of 65 and 59 is associative

LCM of 59 and 65 = LCM of 65 and 59

1. What is the LCM of 59 and 65?

Answer: LCM of 59 and 65 is 3835.

2. What are the Factors of 59?

Answer: Factors of 59 are 1, 59. There are 2 integers that are factors of 59. The greatest factor of 59 is 59.

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 59 and 65?

Answer:

Least Common Multiple of 59 and 65 = 3835

Step 1: Find the prime factorization of 59

59 = 59

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 = 3835 = 5 x 13 x 59

Step 4: Therefore, the least common multiple of 59 and 65 is 3835.