Least Common Multiple of 65 and 67

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

• Least Common Multiple of 65 and 67 by Prime method
• Least Common Multiple of 65 and 67 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 65 and 67. First we will calculate the prime factors of 65 and 67.

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 67

Prime factors of 67 are 67. Prime factorization of 67 in exponential form is:

67 = 67¹

Now multiplying the highest exponent prime factors to calculate the LCM of 65 and 67.

LCM(65,67) = 5¹×13¹×67¹
LCM(65,67) = 4355

Factors of 65

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

1, 5, 13, 65

Factors of 67

List of positive integer factors of 67 that divides 67 without a remainder.

1, 67

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65 and 67, than apply into the LCM equation.

GCF(65,67) = 1
LCM(65,67) = ( 65 × 67) / 1
LCM(65,67) = 4355 / 1
LCM(65,67) = 4355

(i) The LCM of 67 and 65 is associative

LCM of 65 and 67 = LCM of 67 and 65

1. What is the LCM of 65 and 67?

Answer: LCM of 65 and 67 is 4355.

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 67?

Answer: Factors of 67 are 1, 67. There are 2 integers that are factors of 67. The greatest factor of 67 is 67.

4. How to Find the LCM of 65 and 67?

Answer:

Least Common Multiple of 65 and 67 = 4355

Step 1: Find the prime factorization of 65

65 = 5 x 13

Step 2: Find the prime factorization of 67

67 = 67

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

LCM = 4355 = 5 x 13 x 67

Step 4: Therefore, the least common multiple of 65 and 67 is 4355.