Least Common Multiple of 86 and 89

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

• Least Common Multiple of 86 and 89 by Prime method
• Least Common Multiple of 86 and 89 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 86 and 89. First we will calculate the prime factors of 86 and 89.

Prime Factorization of 86

Prime factors of 86 are 2,43. Prime factorization of 86 in exponential form is:

86 = 2¹×43¹

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 86 and 89.

LCM(86,89) = 2¹×43¹×89¹
LCM(86,89) = 7654

Factors of 86

List of positive integer factors of 86 that divides 86 without a remainder.

1, 2, 43, 86

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 86 and 89, than apply into the LCM equation.

GCF(86,89) = 1
LCM(86,89) = ( 86 × 89) / 1
LCM(86,89) = 7654 / 1
LCM(86,89) = 7654

(i) The LCM of 89 and 86 is associative

LCM of 86 and 89 = LCM of 89 and 86

1. What is the LCM of 86 and 89?

Answer: LCM of 86 and 89 is 7654.

2. What are the Factors of 86?

Answer: Factors of 86 are 1, 2, 43, 86. There are 4 integers that are factors of 86. The greatest factor of 86 is 86.

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 86 and 89?

Answer:

Least Common Multiple of 86 and 89 = 7654

Step 1: Find the prime factorization of 86

86 = 2 x 43

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 = 7654 = 2 x 43 x 89

Step 4: Therefore, the least common multiple of 86 and 89 is 7654.