LCM of 144 and 164
5904 is the LCM of 144 and 164. 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 144 and 164, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 144 and 164?
lcm (144 164) = (?)
144 => 2 x 2 x 2 x 2 x 3 x 3
164 => 2 x 2 x 41
= 2 x 2 x 2 x 2 x 3 x 3 x 41
= 5904
lcm (144 and 164) = 5904
5904 is the LCM of 144 and 164.
where,
144 is a positive integer,
164 is a positive integer,
5904 is the LCM of 144 and 164,
{2 x 2} in {2 x 2 x 2 x 2 x 3 x 3, 2 x 2 x 41} are the common factors of 144 and 164,
{2 x 2 x 3 x 3 x 41} in {2 x 2 x 2 x 2 x 3 x 3, 2 x 2 x 41} are the uncommon factors of 144 and 164.
Use in Mathematics: LCM of 144 and 164
The below are some of the mathematical applications where lcm of 144 and 164 can be used:
- to find the least number which is exactly divisible by 144 and 164.
- to find the common denominator for two fractions having 144 and 164 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 144 and 164 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 144 seconds and bell B tolls at 164 seconds repeatedly. The answer is that all bells A and B toll together at 5904 seconds for the first time, at 11808 seconds for the second time, at 17712 seconds for the third time and so on.
Important Notes: 144 and 164 lcm
The below are the important notes to be remembered while solving the lcm of 144 and 164:
- The common prime factors and the remaining prime factors of 144 and 164 should be multiplied to find the least common multiple of 144 and 164, when solving lcm by using prime factors method.
- The results of lcm of 144 and 164, and the lcm of 164 and 144 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 144 and 164?
The below solved example with step by step work shows how to find what is the lcm of 144 and 164 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 144 and 164?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 144
B = 164
What to be found:
find the lcm of 144 and 164
step 2 Find the prime factors of 144 and 164:
Prime factors of 144 = 2 x 2 x 2 x 2 x 3 x 3
Prime factors of 164 = 2 x 2 x 41
step 3 Identify the repeated and non-repeated prime factors of 144 and 164:
{2, 2} are the most repeated factors and {2 x 2 x 3 x 3 x 41} are the non-repeated factors of 144 and 164.
step 4 Find the product of repeated and non-repeated prime factors of 144 and 164:
= 2 x 2 x 2 x 2 x 3 x 3 x 41
= 5904
lcm(144 and 164) = 5904
Hence,
lcm of 144 and 164 is 5904
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 144 and 164.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 144 and 164
What to be found:
lcm (144, 164) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
144 and 164
step 3 Choose the divisor which divides each or most of the given integers (144 and 164), 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 144 and 164 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 144 | 164 |
| 2 | 72 | 82 |
| 2 | 36 | 41 |
| 2 | 18 | 41 |
| 3 | 9 | 41 |
| 3 | 3 | 41 |
| 41 | 1 | 41 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 144 and 164:
= 2 x 2 x 2 x 2 x 3 x 3 x 41
= 5904
LCM(144, 164) = 5904
The LCM of two numbers 144 and 164 is 5904