LCM of 84 and 121
10164 is the LCM of 84 and 121. The step-by-step solution using prime factors and special division methods is one of the simple methods to easily understand how to find what is the LCM of 84 and 121, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 84 and 121?
lcm (84 121) = (?)
84 => 2 x 2 x 3 x 7
121 => 11 x 11
= 2 x 2 x 3 x 7 x 11 x 11
= 10164
lcm (84 and 121) = 10164
10164 is the LCM of 84 and 121.
where,
84 is a positive integer,
121 is a positive integer,
10164 is the LCM of 84 and 121,
There is no common factors of 84 and 121 in {2 x 2 x 3 x 7, 11 x 11},
{2 x 2 x 3 x 7 x 11 x 11} in {2 x 2 x 3 x 7, 11 x 11} are the uncommon factors of 84 and 121.
Use in Mathematics: LCM of 84 and 121
The below are some of the mathematical applications where lcm of 84 and 121 can be used:
- to find the least number which is exactly divisible by 84 and 121.
- to find the common denominator for two fractions having 84 and 121 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 84 and 121 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 84 seconds and bell B tolls at 121 seconds repeatedly. The answer is that all bells A and B toll together at 10164 seconds for the first time, at 20328 seconds for the second time, at 30492 seconds for the third time and so on.
Important Notes: 84 and 121 lcm
The below are the important notes to be remembered while solving the lcm of 84 and 121:
- The common prime factors and the remaining prime factors of 84 and 121 should be multiplied to find the least common multiple of 84 and 121, when solving lcm by using prime factors method.
- The results of lcm of 84 and 121, and the lcm of 121 and 84 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is the LCM of 84 and 121?
The below solved example with step by step work shows how to find what is the lcm of 84 and 121 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 84 and 121?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 84
B = 121
What to be found:
find the lcm of 84 and 121
step 2 Find the prime factors of 84 and 121:
Prime factors of 84 = 2 x 2 x 3 x 7
Prime factors of 121 = 11 x 11
step 3Identify the repeated and non-repeated prime factors of 84 and 121:
Since there is no common factors between 84 and 121, multiplying the given numbers directly provides the LCM of
84 and 121.
= 84 x 121
= 10164
lcm(84 and 121) = 10164
Hence,
lcm of 84 and 121 is 10164
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 84 and 121.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 84 and 121
What to be found:
lcm (84, 121) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
84 and 121
step 3 Choose the divisor which divides each or most of the given integers (84 and 121), 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 84 and 121 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 84 | 121 |
| 2 | 42 | 121 |
| 3 | 21 | 121 |
| 7 | 7 | 121 |
| 11 | 1 | 121 |
| 11 | 1 | 11 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 84 and 121:
= 2 x 2 x 3 x 7 x 11 x 11
= 10164
LCM(84, 121) = 10164
The LCM of two numbers 84 and 121 is 10164