LCM of 169 and 324
54756 is the LCM of 169 and 324. 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 169 and 324, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 169 and 324?
lcm (169 324) = (?)
169 => 13 x 13
324 => 2 x 2 x 3 x 3 x 3 x 3
= 13 x 13 x 2 x 2 x 3 x 3 x 3 x 3
= 54756
lcm (169 and 324) = 54756
54756 is the LCM of 169 and 324.
where,
169 is a positive integer,
324 is a positive integer,
54756 is the LCM of 169 and 324,
There is no common factors of 169 and 324 in {13 x 13, 2 x 2 x 3 x 3 x 3 x 3},
{13 x 13 x 2 x 2 x 3 x 3 x 3 x 3} in {13 x 13, 2 x 2 x 3 x 3 x 3 x 3} are the uncommon factors of 169 and 324.
Use in Mathematics: LCM of 169 and 324
The below are some of the mathematical applications where lcm of 169 and 324 can be used:
- to find the least number which is exactly divisible by 169 and 324.
- to find the common denominator for two fractions having 169 and 324 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 169 and 324 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 169 seconds and bell B tolls at 324 seconds repeatedly. The answer is that all bells A and B toll together at 54756 seconds for the first time, at 109512 seconds for the second time, at 164268 seconds for the third time and so on.
Important Notes: 169 and 324 lcm
The below are the important notes to be remembered while solving the lcm of 169 and 324:
- The common prime factors and the remaining prime factors of 169 and 324 should be multiplied to find the least common multiple of 169 and 324, when solving lcm by using prime factors method.
- The results of lcm of 169 and 324, and the lcm of 324 and 169 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 169 and 324?
The below solved example with step by step work shows how to find what is the lcm of 169 and 324 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 169 and 324?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 169
B = 324
What to be found:
find the lcm of 169 and 324
step 2 Find the prime factors of 169 and 324:
Prime factors of 169 = 13 x 13
Prime factors of 324 = 2 x 2 x 3 x 3 x 3 x 3
step 3Identify the repeated and non-repeated prime factors of 169 and 324:
Since there is no common factors between 169 and 324, multiplying the given numbers directly provides the LCM of
169 and 324.
= 169 x 324
= 54756
lcm(169 and 324) = 54756
Hence,
lcm of 169 and 324 is 54756
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 169 and 324.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 169 and 324
What to be found:
lcm (169, 324) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
169 and 324
step 3 Choose the divisor which divides each or most of the given integers (169 and 324), 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 169 and 324 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 169 | 324 |
| 2 | 169 | 162 |
| 3 | 169 | 81 |
| 3 | 169 | 27 |
| 3 | 169 | 9 |
| 3 | 169 | 3 |
| 13 | 169 | 1 |
| 13 | 13 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 169 and 324:
= 2 x 2 x 3 x 3 x 3 x 3 x 13 x 13
= 54756
LCM(169, 324) = 54756
The LCM of two numbers 169 and 324 is 54756