Least Common Multiple of 83 and 85

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

• Least Common Multiple of 83 and 85 by Prime method
• Least Common Multiple of 83 and 85 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 83 and 85. First we will calculate the prime factors of 83 and 85.

Prime Factorization of 83

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

83 = 83¹

Prime Factorization of 85

Prime factors of 85 are 5,17. Prime factorization of 85 in exponential form is:

85 = 5¹×17¹

Now multiplying the highest exponent prime factors to calculate the LCM of 83 and 85.

LCM(83,85) = 5¹×17¹×83¹
LCM(83,85) = 7055

Factors of 83

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

1, 83

Factors of 85

List of positive integer factors of 85 that divides 85 without a remainder.

1, 5, 17, 85

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 83 and 85, than apply into the LCM equation.

GCF(83,85) = 1
LCM(83,85) = ( 83 × 85) / 1
LCM(83,85) = 7055 / 1
LCM(83,85) = 7055

(i) The LCM of 85 and 83 is associative

LCM of 83 and 85 = LCM of 85 and 83

1. What is the LCM of 83 and 85?

Answer: LCM of 83 and 85 is 7055.

2. 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.

3. What are the Factors of 85?

Answer: Factors of 85 are 1, 5, 17, 85. There are 4 integers that are factors of 85. The greatest factor of 85 is 85.

4. How to Find the LCM of 83 and 85?

Answer:

Least Common Multiple of 83 and 85 = 7055

Step 1: Find the prime factorization of 83

83 = 83

Step 2: Find the prime factorization of 85

85 = 5 x 17

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

LCM = 7055 = 5 x 17 x 83

Step 4: Therefore, the least common multiple of 83 and 85 is 7055.