LCM of 144 and 184
3312 is the LCM of 144 and 184. 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 184, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 144 and 184?
lcm (144 184) = (?)
144 => 2 x 2 x 2 x 2 x 3 x 3
184 => 2 x 2 x 2 x 23
= 2 x 2 x 2 x 2 x 3 x 3 x 23
= 3312
lcm (144 and 184) = 3312
3312 is the LCM of 144 and 184.
where,
144 is a positive integer,
184 is a positive integer,
3312 is the LCM of 144 and 184,
{2 x 2 x 2} in {2 x 2 x 2 x 2 x 3 x 3, 2 x 2 x 2 x 23} are the common factors of 144 and 184,
{2 x 3 x 3 x 23} in {2 x 2 x 2 x 2 x 3 x 3, 2 x 2 x 2 x 23} are the uncommon factors of 144 and 184.
Use in Mathematics: LCM of 144 and 184
The below are some of the mathematical applications where lcm of 144 and 184 can be used:
- to find the least number which is exactly divisible by 144 and 184.
- to find the common denominator for two fractions having 144 and 184 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 144 and 184 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 184 seconds repeatedly. The answer is that all bells A and B toll together at 3312 seconds for the first time, at 6624 seconds for the second time, at 9936 seconds for the third time and so on.
Important Notes: 144 and 184 lcm
The below are the important notes to be remembered while solving the lcm of 144 and 184:
- The common prime factors and the remaining prime factors of 144 and 184 should be multiplied to find the least common multiple of 144 and 184, when solving lcm by using prime factors method.
- The results of lcm of 144 and 184, and the lcm of 184 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 184?
The below solved example with step by step work shows how to find what is the lcm of 144 and 184 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 144 and 184?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 144
B = 184
What to be found:
find the lcm of 144 and 184
step 2 Find the prime factors of 144 and 184:
Prime factors of 144 = 2 x 2 x 2 x 2 x 3 x 3
Prime factors of 184 = 2 x 2 x 2 x 23
step 3 Identify the repeated and non-repeated prime factors of 144 and 184:
{2, 2, 2} are the most repeated factors and {2 x 3 x 3 x 23} are the non-repeated factors of 144 and 184.
step 4 Find the product of repeated and non-repeated prime factors of 144 and 184:
= 2 x 2 x 2 x 2 x 3 x 3 x 23
= 3312
lcm(144 and 184) = 3312
Hence,
lcm of 144 and 184 is 3312
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 144 and 184.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 144 and 184
What to be found:
lcm (144, 184) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
144 and 184
step 3 Choose the divisor which divides each or most of the given integers (144 and 184), 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 184 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 144 | 184 |
| 2 | 72 | 92 |
| 2 | 36 | 46 |
| 2 | 18 | 23 |
| 3 | 9 | 23 |
| 3 | 3 | 23 |
| 23 | 1 | 23 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 144 and 184:
= 2 x 2 x 2 x 2 x 3 x 3 x 23
= 3312
LCM(144, 184) = 3312
The LCM of two numbers 144 and 184 is 3312