Least Common Multiple of 82 and 83

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Free LCM Calculator determines the least common multiple (LCM) between 82 and 83 the smallest integer that is 6806 that is divisible by both numbers.

Least Common Multiple (LCM) of 82 and 83 is 6806.

LCM(82,83) = 6806

LCM of 82 and 83

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

LCM of:
and

Least Common Multiple of 82 and 83

LCM of 82 and 83 is 6806

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


2 82
41 41
1

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

82 = 21×411

Prime Factorization of 83


83 83
1

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

Least Common Multiple of 82 and 83 with GCF Formula

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

Properties of LCM 82 and 83

(i) The LCM of 83 and 82 is associative

LCM of 82 and 83 = LCM of 83 and 82

Frequently Asked Questions on LCM of 82 and 83

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.