LCM of 252 and 339
28476 is the LCM of 252 and 339. 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 339, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 252 and 339?
lcm (252 339) = (?)
252 => 2 x 2 x 3 x 3 x 7
339 => 3 x 113
= 3 x 2 x 2 x 3 x 7 x 113
= 28476
lcm (252 and 339) = 28476
28476 is the LCM of 252 and 339.
where,
252 is a positive integer,
339 is a positive integer,
28476 is the LCM of 252 and 339,
{3} in {2 x 2 x 3 x 3 x 7, 3 x 113} is the common factors of 252 and 339,
{2 x 2 x 3 x 7 x 113} in {2 x 2 x 3 x 3 x 7, 3 x 113} are the uncommon factors of 252 and 339.
Use in Mathematics: LCM of 252 and 339
The below are some of the mathematical applications where lcm of 252 and 339 can be used:
- to find the least number which is exactly divisible by 252 and 339.
- to find the common denominator for two fractions having 252 and 339 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 252 and 339 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 339 seconds repeatedly. The answer is that all bells A and B toll together at 28476 seconds for the first time, at 56952 seconds for the second time, at 85428 seconds for the third time and so on.
Important Notes: 252 and 339 lcm
The below are the important notes to be remembered while solving the lcm of 252 and 339:
- The common prime factors and the remaining prime factors of 252 and 339 should be multiplied to find the least common multiple of 252 and 339, when solving lcm by using prime factors method.
- The results of lcm of 252 and 339, and the lcm of 339 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 339?
The below solved example with step by step work shows how to find what is the lcm of 252 and 339 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 252 and 339?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 252
B = 339
What to be found:
find the lcm of 252 and 339
step 2 Find the prime factors of 252 and 339:
Prime factors of 252 = 2 x 2 x 3 x 3 x 7
Prime factors of 339 = 3 x 113
step 3 Identify the repeated and non-repeated prime factors of 252 and 339:
{3} is the most repeated factor and {2 x 2 x 3 x 7 x 113} are the non-repeated factors of 252 and 339.
step 4 Find the product of repeated and non-repeated prime factors of 252 and 339:
= 3 x 2 x 2 x 3 x 7 x 113
= 28476
lcm(252 and 339) = 28476
Hence,
lcm of 252 and 339 is 28476
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 252 and 339.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 252 and 339
What to be found:
lcm (252, 339) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
252 and 339
step 3 Choose the divisor which divides each or most of the given integers (252 and 339), 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 339 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 252 | 339 |
| 2 | 126 | 339 |
| 3 | 63 | 339 |
| 3 | 21 | 113 |
| 7 | 7 | 113 |
| 113 | 1 | 113 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 252 and 339:
= 2 x 2 x 3 x 3 x 7 x 113
= 28476
LCM(252, 339) = 28476
The LCM of two numbers 252 and 339 is 28476