Least Common Multiple of 87 and 89

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

• Least Common Multiple of 87 and 89 by Prime method
• Least Common Multiple of 87 and 89 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 87 and 89. First we will calculate the prime factors of 87 and 89.

Prime Factorization of 87

Prime factors of 87 are 3,29. Prime factorization of 87 in exponential form is:

87 = 3¹×29¹

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 87 and 89.

LCM(87,89) = 3¹×29¹×89¹
LCM(87,89) = 7743

Factors of 87

List of positive integer factors of 87 that divides 87 without a remainder.

1, 3, 29, 87

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 87 and 89, than apply into the LCM equation.

GCF(87,89) = 1
LCM(87,89) = ( 87 × 89) / 1
LCM(87,89) = 7743 / 1
LCM(87,89) = 7743

(i) The LCM of 89 and 87 is associative

LCM of 87 and 89 = LCM of 89 and 87

1. What is the LCM of 87 and 89?

Answer: LCM of 87 and 89 is 7743.

2. What are the Factors of 87?

Answer: Factors of 87 are 1, 3, 29, 87. There are 4 integers that are factors of 87. The greatest factor of 87 is 87.

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 87 and 89?

Answer:

Least Common Multiple of 87 and 89 = 7743

Step 1: Find the prime factorization of 87

87 = 3 x 29

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 = 7743 = 3 x 29 x 89

Step 4: Therefore, the least common multiple of 87 and 89 is 7743.