Least Common Multiple of 85 and 89

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

• Least Common Multiple of 85 and 89 by Prime method
• Least Common Multiple of 85 and 89 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 85 and 89. First we will calculate the prime factors of 85 and 89.

Prime Factorization of 85

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

85 = 5¹×17¹

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 85 and 89.

LCM(85,89) = 5¹×17¹×89¹
LCM(85,89) = 7565

Factors of 85

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

1, 5, 17, 85

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 85 and 89, than apply into the LCM equation.

GCF(85,89) = 1
LCM(85,89) = ( 85 × 89) / 1
LCM(85,89) = 7565 / 1
LCM(85,89) = 7565

(i) The LCM of 89 and 85 is associative

LCM of 85 and 89 = LCM of 89 and 85

1. What is the LCM of 85 and 89?

Answer: LCM of 85 and 89 is 7565.

2. 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.

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 85 and 89?

Answer:

Least Common Multiple of 85 and 89 = 7565

Step 1: Find the prime factorization of 85

85 = 5 x 17

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 = 7565 = 5 x 17 x 89

Step 4: Therefore, the least common multiple of 85 and 89 is 7565.