Least Common Multiple of 82 and 83

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

• Least Common Multiple of 82 and 83 by Prime method
• Least Common Multiple of 82 and 83 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 82 and 83. First we will calculate the prime factors of 82 and 83.

Prime Factorization of 82

Prime factors of 82 are 2,41. Prime factorization of 82 in exponential form is:

82 = 2¹×41¹

Prime Factorization of 83

Prime factors of 83 are 83. Prime factorization of 83 in exponential form is:

83 = 83¹

Now multiplying the highest exponent prime factors to calculate the LCM of 82 and 83.

LCM(82,83) = 2¹×41¹×83¹
LCM(82,83) = 6806

Factors of 82

List of positive integer factors of 82 that divides 82 without a remainder.

1, 2, 41, 82

Factors of 83

List of positive integer factors of 83 that divides 83 without a remainder.

1, 83

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82 and 83, than apply into the LCM equation.

GCF(82,83) = 1
LCM(82,83) = ( 82 × 83) / 1
LCM(82,83) = 6806 / 1
LCM(82,83) = 6806

(i) The LCM of 83 and 82 is associative

LCM of 82 and 83 = LCM of 83 and 82

1. What is the LCM of 82 and 83?

Answer: LCM of 82 and 83 is 6806.

2. What are the Factors of 82?

Answer: Factors of 82 are 1, 2, 41, 82. There are 4 integers that are factors of 82. The greatest factor of 82 is 82.

3. What are the Factors of 83?

Answer: Factors of 83 are 1, 83. There are 2 integers that are factors of 83. The greatest factor of 83 is 83.

4. How to Find the LCM of 82 and 83?

Answer:

Least Common Multiple of 82 and 83 = 6806

Step 1: Find the prime factorization of 82

82 = 2 x 41

Step 2: Find the prime factorization of 83

83 = 83

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

LCM = 6806 = 2 x 41 x 83

Step 4: Therefore, the least common multiple of 82 and 83 is 6806.