LCM of 81 and 84 is equal to 2268. The comprehensive work provides more insight of how to find what is the lcm of 81 and 84 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

__what is the lcm of 81 and 84?__

lcm (81 84) = (?)

81 => **3 x 3 x 3 x 3**

84 => **2 x 2 x 3 x 7**

= 3 x 3 x 3 x 3 x 2 x 2 x 7

= 2268

lcm (81 and 84) = 2268

**2268 is the lcm of 81 and 84.**

__where,__

81 is a positive integer,

84 is a positive integer,

2268 is the lcm of 81 and 84,

{3} in {3 x 3 x 3 x 3, 2 x 2 x 3 x 7} is the common factors of 81 and 84,

{3 x 3 x 3 x 2 x 2 x 7} in {3 x 3 x 3 x 3, 2 x 2 x 3 x 7} are the uncommon factors of 81 and 84.

__Use in Mathematics: LCM of 81 and 84__

The below are some of the mathematical applications where lcm of 81 and 84 can be used:

- to find the least number which is exactly divisible by 81 and 84.
- to find the common denominator for two fractions having 81 and 84 as denominators in the unlike fractions addition or subtraction.

In the context of lcm real world problems, the lcm of 81 and 84 helps to find the exact time when two similar and recurring events with different time schedule happens together at the same time. For example, the real world problems involve lcm in situations to find at what time the bells A and B all toll together, if bell A tolls at 81 seconds and bell B tolls at 84 seconds repeatedly. The answer is that all bells A and B toll together at 2268 seconds for the first time, at 4536 seconds for the second time, at 6804 seconds for the third time and so on.

The below are the important notes to be remembered while solving the lcm of 81 and 84:

- The common prime factors and the remaining prime factors of 81 and 84 should be multiplied to find the least common multiple of 81 and 84, when solving lcm by using prime factors method.
- The results of lcm of 81 and 84, and the lcm of 84 and 81 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.

The below solved example with step by step work shows how to find what is the lcm of 81 and 84 by using prime factors method and division method.

__Solved example using prime factors method:__

What is the LCM of 81 and 84?

step 1
Address the input parameters, values and observe what to be found:

__Input parameters and values:__

A = 81

B = 84

__What to be found:__

find the lcm of 81 and 84

step 2 Find the prime factors of 81 and 84:

Prime factors of 81 = 3 x 3 x 3 x 3

Prime factors of 84 = 2 x 2 x 3 x 7

step 3 Identify the repeated and non-repeated prime factors of 81 and 84:

{3} is the most repeated factor and {3 x 3 x 3 x 2 x 2 x 7} are the non-repeated factors of 81 and 84.

step 4 Find the product of repeated and non-repeated prime factors of 81 and 84:

= 3 x 3 x 3 x 3 x 2 x 2 x 7

= 2268

lcm(81 and 84) = 2268

Hence,

lcm of 81 and 84 is 2268

This special division method is the easiest way to understand the entire calculation of what is the lcm of 81 and 84.

step 1 Address the input parameters, values and observe what to be found:

Integers: 81 and 84

lcm (81, 84) = ?

step 2 Arrange the given integers in the horizontal form with space or comma separated format:

81 and 84

step 3 Choose the divisor which divides each or most of the given integers (81 and 84), divide each integers separately and write down the quotient in the next line right under the respective integers. Bring down the integer to the next line if any integer in 81 and 84 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

2 | 81 | 84 |

2 | 81 | 42 |

3 | 81 | 21 |

3 | 27 | 7 |

3 | 9 | 7 |

3 | 3 | 7 |

7 | 1 | 7 |

1 | 1 |

step 4 Multiply the divisors to find the lcm of 81 and 84:

= 2 x 2 x 3 x 3 x 3 x 3 x 7

= 2268

LCM(81, 84) = 2268

The least common multiple for two numbers 81 and 84 is 2268