LCM of 135 and 252
3780 is the LCM of 135 and 252. 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 135 and 252, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 135 and 252?
lcm (135 252) = (?)
135 => 3 x 3 x 3 x 5
252 => 2 x 2 x 3 x 3 x 7
= 3 x 3 x 3 x 5 x 2 x 2 x 7
= 3780
lcm (135 and 252) = 3780
3780 is the LCM of 135 and 252.
where,
135 is a positive integer,
252 is a positive integer,
3780 is the LCM of 135 and 252,
{3 x 3} in {3 x 3 x 3 x 5, 2 x 2 x 3 x 3 x 7} are the common factors of 135 and 252,
{3 x 5 x 2 x 2 x 7} in {3 x 3 x 3 x 5, 2 x 2 x 3 x 3 x 7} are the uncommon factors of 135 and 252.
Use in Mathematics: LCM of 135 and 252
The below are some of the mathematical applications where lcm of 135 and 252 can be used:
- to find the least number which is exactly divisible by 135 and 252.
- to find the common denominator for two fractions having 135 and 252 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 135 and 252 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 135 seconds and bell B tolls at 252 seconds repeatedly. The answer is that all bells A and B toll together at 3780 seconds for the first time, at 7560 seconds for the second time, at 11340 seconds for the third time and so on.
Important Notes: 135 and 252 lcm
The below are the important notes to be remembered while solving the lcm of 135 and 252:
- The common prime factors and the remaining prime factors of 135 and 252 should be multiplied to find the least common multiple of 135 and 252, when solving lcm by using prime factors method.
- The results of lcm of 135 and 252, and the lcm of 252 and 135 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 135 and 252?
The below solved example with step by step work shows how to find what is the lcm of 135 and 252 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 135 and 252?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 135
B = 252
What to be found:
find the lcm of 135 and 252
step 2 Find the prime factors of 135 and 252:
Prime factors of 135 = 3 x 3 x 3 x 5
Prime factors of 252 = 2 x 2 x 3 x 3 x 7
step 3 Identify the repeated and non-repeated prime factors of 135 and 252:
{3, 3} are the most repeated factors and {3 x 5 x 2 x 2 x 7} are the non-repeated factors of 135 and 252.
step 4 Find the product of repeated and non-repeated prime factors of 135 and 252:
= 3 x 3 x 3 x 5 x 2 x 2 x 7
= 3780
lcm(135 and 252) = 3780
Hence,
lcm of 135 and 252 is 3780
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 135 and 252.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 135 and 252
What to be found:
lcm (135, 252) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
135 and 252
step 3 Choose the divisor which divides each or most of the given integers (135 and 252), 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 135 and 252 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 135 | 252 |
| 2 | 135 | 126 |
| 3 | 135 | 63 |
| 3 | 45 | 21 |
| 3 | 15 | 7 |
| 5 | 5 | 7 |
| 7 | 1 | 7 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 135 and 252:
= 2 x 2 x 3 x 3 x 3 x 5 x 7
= 3780
LCM(135, 252) = 3780
The LCM of two numbers 135 and 252 is 3780