Least Common Multiple of 84 and 87

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 84 and 87 the smallest integer that is 2436 that is divisible by both numbers.

Least Common Multiple (LCM) of 84 and 87 is 2436.

LCM(84,87) = 2436

LCM of 84 and 87

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

LCM of:
and

Least Common Multiple of 84 and 87

LCM of 84 and 87 is 2436

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 87. First we will calculate the prime factors of 84 and 87.

Prime Factorization of 84


2 84
2 42
3 21
7 7
1

Prime factors of 84 are 2, 3,7. Prime factorization of 84 in exponential form is:

84 = 22×31×71

Prime Factorization of 87


3 87
29 29
1

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 84 and 87.

LCM(84,87) = 22×31×71×291
LCM(84,87) = 2436

Factors of 84

List of positive integer factors of 84 that divides 84 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Factors of 87

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

1, 3, 29, 87

Least Common Multiple of 84 and 87 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84 and 87, than apply into the LCM equation.

GCF(84,87) = 3
LCM(84,87) = ( 84 × 87) / 3
LCM(84,87) = 7308 / 3
LCM(84,87) = 2436

Properties of LCM 84 and 87

(i) The LCM of 87 and 84 is associative

LCM of 84 and 87 = LCM of 87 and 84

Related Least Common Multiples of 84

Related Least Common Multiples of 87

Frequently Asked Questions on LCM of 84 and 87

1. What is the LCM of 84 and 87?

Answer: LCM of 84 and 87 is 2436.

2. What are the Factors of 84?

Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.

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 84 and 87?

Answer:

Least Common Multiple of 84 and 87 = 2436

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

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 = 2436 = 2 x 2 x 3 x 7 x 29

Step 4: Therefore, the least common multiple of 84 and 87 is 2436.