Least Common Multiple of 82 and 89

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

• Least Common Multiple of 82 and 89 by Prime method
• Least Common Multiple of 82 and 89 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 82 and 89. First we will calculate the prime factors of 82 and 89.

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 89

Prime factors of 89 are 89. Prime factorization of 89 in exponential form is:

89 = 89¹

Now multiplying the highest exponent prime factors to calculate the LCM of 82 and 89.

LCM(82,89) = 2¹×41¹×89¹
LCM(82,89) = 7298

Factors of 82

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

1, 2, 41, 82

Factors of 89

List of positive integer factors of 89 that divides 89 without a remainder.

1, 89

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82 and 89, than apply into the LCM equation.

GCF(82,89) = 1
LCM(82,89) = ( 82 × 89) / 1
LCM(82,89) = 7298 / 1
LCM(82,89) = 7298

(i) The LCM of 89 and 82 is associative

LCM of 82 and 89 = LCM of 89 and 82

1. What is the LCM of 82 and 89?

Answer: LCM of 82 and 89 is 7298.

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 89?

Answer: Factors of 89 are 1, 89. There are 2 integers that are factors of 89. The greatest factor of 89 is 89.

4. How to Find the LCM of 82 and 89?

Answer:

Least Common Multiple of 82 and 89 = 7298

Step 1: Find the prime factorization of 82

82 = 2 x 41

Step 2: Find the prime factorization of 89

89 = 89

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

LCM = 7298 = 2 x 41 x 89

Step 4: Therefore, the least common multiple of 82 and 89 is 7298.