LCM of 132 and 296
9768 is the LCM of 132 and 296. 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 132 and 296, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 132 and 296?
lcm (132 296) = (?)
132 => 2 x 2 x 3 x 11
296 => 2 x 2 x 2 x 37
= 2 x 2 x 3 x 11 x 2 x 37
= 9768
lcm (132 and 296) = 9768
9768 is the LCM of 132 and 296.
where,
132 is a positive integer,
296 is a positive integer,
9768 is the LCM of 132 and 296,
{2 x 2} in {2 x 2 x 3 x 11, 2 x 2 x 2 x 37} are the common factors of 132 and 296,
{3 x 11 x 2 x 37} in {2 x 2 x 3 x 11, 2 x 2 x 2 x 37} are the uncommon factors of 132 and 296.
Use in Mathematics: LCM of 132 and 296
The below are some of the mathematical applications where lcm of 132 and 296 can be used:
- to find the least number which is exactly divisible by 132 and 296.
- to find the common denominator for two fractions having 132 and 296 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 132 and 296 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 132 seconds and bell B tolls at 296 seconds repeatedly. The answer is that all bells A and B toll together at 9768 seconds for the first time, at 19536 seconds for the second time, at 29304 seconds for the third time and so on.
Important Notes: 132 and 296 lcm
The below are the important notes to be remembered while solving the lcm of 132 and 296:
- The common prime factors and the remaining prime factors of 132 and 296 should be multiplied to find the least common multiple of 132 and 296, when solving lcm by using prime factors method.
- The results of lcm of 132 and 296, and the lcm of 296 and 132 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 132 and 296?
The below solved example with step by step work shows how to find what is the lcm of 132 and 296 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 132 and 296?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 132
B = 296
What to be found:
find the lcm of 132 and 296
step 2 Find the prime factors of 132 and 296:
Prime factors of 132 = 2 x 2 x 3 x 11
Prime factors of 296 = 2 x 2 x 2 x 37
step 3 Identify the repeated and non-repeated prime factors of 132 and 296:
{2, 2} are the most repeated factors and {3 x 11 x 2 x 37} are the non-repeated factors of 132 and 296.
step 4 Find the product of repeated and non-repeated prime factors of 132 and 296:
= 2 x 2 x 3 x 11 x 2 x 37
= 9768
lcm(132 and 296) = 9768
Hence,
lcm of 132 and 296 is 9768
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 132 and 296.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 132 and 296
What to be found:
lcm (132, 296) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
132 and 296
step 3 Choose the divisor which divides each or most of the given integers (132 and 296), 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 132 and 296 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 132 | 296 |
| 2 | 66 | 148 |
| 2 | 33 | 74 |
| 3 | 33 | 37 |
| 11 | 11 | 37 |
| 37 | 1 | 37 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 132 and 296:
= 2 x 2 x 2 x 3 x 11 x 37
= 9768
LCM(132, 296) = 9768
The LCM of two numbers 132 and 296 is 9768