Least Common Multiple of 81 and 84

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 81 and 84 the smallest integer that is 2268 that is divisible by both numbers.

Least Common Multiple (LCM) of 81 and 84 is 2268.

LCM(81,84) = 2268

LCM of 81 and 84

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

LCM of:
and

Least Common Multiple of 81 and 84

LCM of 81 and 84 is 2268

Least common multiple can be found by multiplying the highest exponent prime factors of 81 and 84. First we will calculate the prime factors of 81 and 84.

Prime Factorization of 81


3 81
3 27
3 9
3 3
1

Prime factors of 81 are 3. Prime factorization of 81 in exponential form is:

81 = 34

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

Now multiplying the highest exponent prime factors to calculate the LCM of 81 and 84.

LCM(81,84) = 22×34×71
LCM(81,84) = 2268

Factors of 81

List of positive integer factors of 81 that divides 81 without a remainder.

1, 3, 9, 27, 81

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

Least Common Multiple of 81 and 84 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 81 and 84, than apply into the LCM equation.

GCF(81,84) = 3
LCM(81,84) = ( 81 × 84) / 3
LCM(81,84) = 6804 / 3
LCM(81,84) = 2268

Properties of LCM 81 and 84

(i) The LCM of 84 and 81 is associative

LCM of 81 and 84 = LCM of 84 and 81

Related Least Common Multiples of 81

Related Least Common Multiples of 84

Frequently Asked Questions on LCM of 81 and 84

1. What is the LCM of 81 and 84?

Answer: LCM of 81 and 84 is 2268.

2. What are the Factors of 81?

Answer: Factors of 81 are 1, 3, 9, 27, 81. There are 5 integers that are factors of 81. The greatest factor of 81 is 81.

3. 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.

4. How to Find the LCM of 81 and 84?

Answer:

Least Common Multiple of 81 and 84 = 2268

Step 1: Find the prime factorization of 81

81 = 3 x 3 x 3 x 3

Step 2: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

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

LCM = 2268 = 2 x 2 x 3 x 3 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 81 and 84 is 2268.