LCM of 126 and 243
3402 is the LCM of 126 and 243. 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 126 and 243, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 126 and 243?
lcm (126 243) = (?)
126 => 2 x 3 x 3 x 7
243 => 3 x 3 x 3 x 3 x 3
= 3 x 3 x 2 x 7 x 3 x 3 x 3
= 3402
lcm (126 and 243) = 3402
3402 is the LCM of 126 and 243.
where,
126 is a positive integer,
243 is a positive integer,
3402 is the LCM of 126 and 243,
{3 x 3} in {2 x 3 x 3 x 7, 3 x 3 x 3 x 3 x 3} are the common factors of 126 and 243,
{2 x 7 x 3 x 3 x 3} in {2 x 3 x 3 x 7, 3 x 3 x 3 x 3 x 3} are the uncommon factors of 126 and 243.
Use in Mathematics: LCM of 126 and 243
The below are some of the mathematical applications where lcm of 126 and 243 can be used:
- to find the least number which is exactly divisible by 126 and 243.
- to find the common denominator for two fractions having 126 and 243 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 126 and 243 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 126 seconds and bell B tolls at 243 seconds repeatedly. The answer is that all bells A and B toll together at 3402 seconds for the first time, at 6804 seconds for the second time, at 10206 seconds for the third time and so on.
Important Notes: 126 and 243 lcm
The below are the important notes to be remembered while solving the lcm of 126 and 243:
- The common prime factors and the remaining prime factors of 126 and 243 should be multiplied to find the least common multiple of 126 and 243, when solving lcm by using prime factors method.
- The results of lcm of 126 and 243, and the lcm of 243 and 126 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 126 and 243?
The below solved example with step by step work shows how to find what is the lcm of 126 and 243 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 126 and 243?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 126
B = 243
What to be found:
find the lcm of 126 and 243
step 2 Find the prime factors of 126 and 243:
Prime factors of 126 = 2 x 3 x 3 x 7
Prime factors of 243 = 3 x 3 x 3 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 126 and 243:
{3, 3} are the most repeated factors and {2 x 7 x 3 x 3 x 3} are the non-repeated factors of 126 and 243.
step 4 Find the product of repeated and non-repeated prime factors of 126 and 243:
= 3 x 3 x 2 x 7 x 3 x 3 x 3
= 3402
lcm(126 and 243) = 3402
Hence,
lcm of 126 and 243 is 3402
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 126 and 243.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 126 and 243
What to be found:
lcm (126, 243) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
126 and 243
step 3 Choose the divisor which divides each or most of the given integers (126 and 243), 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 126 and 243 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 126 | 243 |
| 3 | 63 | 243 |
| 3 | 21 | 81 |
| 3 | 7 | 27 |
| 3 | 7 | 9 |
| 3 | 7 | 3 |
| 7 | 7 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 126 and 243:
= 2 x 3 x 3 x 3 x 3 x 3 x 7
= 3402
LCM(126, 243) = 3402
The LCM of two numbers 126 and 243 is 3402