Least Common Multiple of 83 and 87

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

• Least Common Multiple of 83 and 87 by Prime method
• Least Common Multiple of 83 and 87 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 83 and 87. First we will calculate the prime factors of 83 and 87.

Prime Factorization of 83

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

83 = 83¹

Prime Factorization of 87

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

87 = 3¹×29¹

Now multiplying the highest exponent prime factors to calculate the LCM of 83 and 87.

LCM(83,87) = 3¹×29¹×83¹
LCM(83,87) = 7221

Factors of 83

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

1, 83

Factors of 87

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

1, 3, 29, 87

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 83 and 87, than apply into the LCM equation.

GCF(83,87) = 1
LCM(83,87) = ( 83 × 87) / 1
LCM(83,87) = 7221 / 1
LCM(83,87) = 7221

(i) The LCM of 87 and 83 is associative

LCM of 83 and 87 = LCM of 87 and 83

1. What is the LCM of 83 and 87?

Answer: LCM of 83 and 87 is 7221.

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 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.

4. How to Find the LCM of 83 and 87?

Answer:

Least Common Multiple of 83 and 87 = 7221

Step 1: Find the prime factorization of 83

83 = 83

Step 2: Find the prime factorization of 87

87 = 3 x 29

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

LCM = 7221 = 3 x 29 x 83

Step 4: Therefore, the least common multiple of 83 and 87 is 7221.