LCM of 252 and 356
22428 is the LCM of 252 and 356. 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 252 and 356, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 252 and 356?
lcm (252 356) = (?)
252 => 2 x 2 x 3 x 3 x 7
356 => 2 x 2 x 89
= 2 x 2 x 3 x 3 x 7 x 89
= 22428
lcm (252 and 356) = 22428
22428 is the LCM of 252 and 356.
where,
252 is a positive integer,
356 is a positive integer,
22428 is the LCM of 252 and 356,
{2 x 2} in {2 x 2 x 3 x 3 x 7, 2 x 2 x 89} are the common factors of 252 and 356,
{3 x 3 x 7 x 89} in {2 x 2 x 3 x 3 x 7, 2 x 2 x 89} are the uncommon factors of 252 and 356.
Use in Mathematics: LCM of 252 and 356
The below are some of the mathematical applications where lcm of 252 and 356 can be used:
- to find the least number which is exactly divisible by 252 and 356.
- to find the common denominator for two fractions having 252 and 356 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 252 and 356 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 252 seconds and bell B tolls at 356 seconds repeatedly. The answer is that all bells A and B toll together at 22428 seconds for the first time, at 44856 seconds for the second time, at 67284 seconds for the third time and so on.
Important Notes: 252 and 356 lcm
The below are the important notes to be remembered while solving the lcm of 252 and 356:
- The common prime factors and the remaining prime factors of 252 and 356 should be multiplied to find the least common multiple of 252 and 356, when solving lcm by using prime factors method.
- The results of lcm of 252 and 356, and the lcm of 356 and 252 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 252 and 356?
The below solved example with step by step work shows how to find what is the lcm of 252 and 356 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 252 and 356?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 252
B = 356
What to be found:
find the lcm of 252 and 356
step 2 Find the prime factors of 252 and 356:
Prime factors of 252 = 2 x 2 x 3 x 3 x 7
Prime factors of 356 = 2 x 2 x 89
step 3 Identify the repeated and non-repeated prime factors of 252 and 356:
{2, 2} are the most repeated factors and {3 x 3 x 7 x 89} are the non-repeated factors of 252 and 356.
step 4 Find the product of repeated and non-repeated prime factors of 252 and 356:
= 2 x 2 x 3 x 3 x 7 x 89
= 22428
lcm(252 and 356) = 22428
Hence,
lcm of 252 and 356 is 22428
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 252 and 356.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 252 and 356
What to be found:
lcm (252, 356) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
252 and 356
step 3 Choose the divisor which divides each or most of the given integers (252 and 356), 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 252 and 356 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 252 | 356 |
| 2 | 126 | 178 |
| 3 | 63 | 89 |
| 3 | 21 | 89 |
| 7 | 7 | 89 |
| 89 | 1 | 89 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 252 and 356:
= 2 x 2 x 3 x 3 x 7 x 89
= 22428
LCM(252, 356) = 22428
The LCM of two numbers 252 and 356 is 22428