LCM of 84 and 169
14196 is the LCM of 84 and 169. 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 169, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 84 and 169?
lcm (84 169) = (?)
84 => 2 x 2 x 3 x 7
169 => 13 x 13
= 2 x 2 x 3 x 7 x 13 x 13
= 14196
lcm (84 and 169) = 14196
14196 is the LCM of 84 and 169.
where,
84 is a positive integer,
169 is a positive integer,
14196 is the LCM of 84 and 169,
There is no common factors of 84 and 169 in {2 x 2 x 3 x 7, 13 x 13},
{2 x 2 x 3 x 7 x 13 x 13} in {2 x 2 x 3 x 7, 13 x 13} are the uncommon factors of 84 and 169.
Use in Mathematics: LCM of 84 and 169
The below are some of the mathematical applications where lcm of 84 and 169 can be used:
- to find the least number which is exactly divisible by 84 and 169.
- to find the common denominator for two fractions having 84 and 169 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 84 and 169 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 169 seconds repeatedly. The answer is that all bells A and B toll together at 14196 seconds for the first time, at 28392 seconds for the second time, at 42588 seconds for the third time and so on.
Important Notes: 84 and 169 lcm
The below are the important notes to be remembered while solving the lcm of 84 and 169:
- The common prime factors and the remaining prime factors of 84 and 169 should be multiplied to find the least common multiple of 84 and 169, when solving lcm by using prime factors method.
- The results of lcm of 84 and 169, and the lcm of 169 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 169?
The below solved example with step by step work shows how to find what is the lcm of 84 and 169 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 84 and 169?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 84
B = 169
What to be found:
find the lcm of 84 and 169
step 2 Find the prime factors of 84 and 169:
Prime factors of 84 = 2 x 2 x 3 x 7
Prime factors of 169 = 13 x 13
step 3Identify the repeated and non-repeated prime factors of 84 and 169:
Since there is no common factors between 84 and 169, multiplying the given numbers directly provides the LCM of
84 and 169.
= 84 x 169
= 14196
lcm(84 and 169) = 14196
Hence,
lcm of 84 and 169 is 14196
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 84 and 169.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 84 and 169
What to be found:
lcm (84, 169) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
84 and 169
step 3 Choose the divisor which divides each or most of the given integers (84 and 169), 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 169 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 84 | 169 |
| 2 | 42 | 169 |
| 3 | 21 | 169 |
| 7 | 7 | 169 |
| 13 | 1 | 169 |
| 13 | 1 | 13 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 84 and 169:
= 2 x 2 x 3 x 7 x 13 x 13
= 14196
LCM(84, 169) = 14196
The LCM of two numbers 84 and 169 is 14196