LCM of 3 and 144
144 is the LCM of 3 and 144. 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 3 and 144, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 3 and 144?
lcm (3 144) = (?)
3 => 3
144 => 2 x 2 x 2 x 2 x 3 x 3
= 3 x 2 x 2 x 2 x 2 x 3
= 144
lcm (3 and 144) = 144
144 is the LCM of 3 and 144.
where,
3 is a positive integer,
144 is a positive integer,
144 is the LCM of 3 and 144,
{3} in {3, 2 x 2 x 2 x 2 x 3 x 3} is the common factors of 3 and 144,
{2 x 2 x 2 x 2 x 3} in {3, 2 x 2 x 2 x 2 x 3 x 3} are the uncommon factors of 3 and 144.
Use in Mathematics: LCM of 3 and 144
The below are some of the mathematical applications where lcm of 3 and 144 can be used:
- to find the least number which is exactly divisible by 3 and 144.
- to find the common denominator for two fractions having 3 and 144 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 3 and 144 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 3 seconds and bell B tolls at 144 seconds repeatedly. The answer is that all bells A and B toll together at 144 seconds for the first time, at 288 seconds for the second time, at 432 seconds for the third time and so on.
Important Notes: 3 and 144 lcm
The below are the important notes to be remembered while solving the lcm of 3 and 144:
- The common prime factors and the remaining prime factors of 3 and 144 should be multiplied to find the least common multiple of 3 and 144, when solving lcm by using prime factors method.
- The results of lcm of 3 and 144, and the lcm of 144 and 3 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 3 and 144?
The below solved example with step by step work shows how to find what is the lcm of 3 and 144 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 3 and 144?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 3
B = 144
What to be found:
find the lcm of 3 and 144
step 2 Find the prime factors of 3 and 144:
Prime factors of 3 = 3
Prime factors of 144 = 2 x 2 x 2 x 2 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 3 and 144:
{3} is the most repeated factor and {2 x 2 x 2 x 2 x 3} are the non-repeated factors of 3 and 144.
step 4 Find the product of repeated and non-repeated prime factors of 3 and 144:
= 3 x 2 x 2 x 2 x 2 x 3
= 144
lcm(3 and 144) = 144
Hence,
lcm of 3 and 144 is 144
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 3 and 144.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 3 and 144
What to be found:
lcm (3, 144) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
3 and 144
step 3 Choose the divisor which divides each or most of the given integers (3 and 144), 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 3 and 144 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 3 | 144 |
| 2 | 3 | 72 |
| 2 | 3 | 36 |
| 2 | 3 | 18 |
| 3 | 3 | 9 |
| 3 | 1 | 3 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 3 and 144:
= 2 x 2 x 2 x 2 x 3 x 3
= 144
LCM(3, 144) = 144
The LCM of two numbers 3 and 144 is 144