LCM of 54 and 126
378 is the LCM of 54 and 126. 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 54 and 126, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 54 and 126?
lcm (54 126) = (?)
54 => 2 x 3 x 3 x 3
126 => 2 x 3 x 3 x 7
= 2 x 3 x 3 x 3 x 7
= 378
lcm (54 and 126) = 378
378 is the LCM of 54 and 126.
where,
54 is a positive integer,
126 is a positive integer,
378 is the LCM of 54 and 126,
{2 x 3 x 3} in {2 x 3 x 3 x 3, 2 x 3 x 3 x 7} are the common factors of 54 and 126,
{3 x 7} in {2 x 3 x 3 x 3, 2 x 3 x 3 x 7} are the uncommon factors of 54 and 126.
Use in Mathematics: LCM of 54 and 126
The below are some of the mathematical applications where lcm of 54 and 126 can be used:
- to find the least number which is exactly divisible by 54 and 126.
- to find the common denominator for two fractions having 54 and 126 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 54 and 126 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 54 seconds and bell B tolls at 126 seconds repeatedly. The answer is that all bells A and B toll together at 378 seconds for the first time, at 756 seconds for the second time, at 1134 seconds for the third time and so on.
Important Notes: 54 and 126 lcm
The below are the important notes to be remembered while solving the lcm of 54 and 126:
- The common prime factors and the remaining prime factors of 54 and 126 should be multiplied to find the least common multiple of 54 and 126, when solving lcm by using prime factors method.
- The results of lcm of 54 and 126, and the lcm of 126 and 54 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 54 and 126?
The below solved example with step by step work shows how to find what is the lcm of 54 and 126 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 54 and 126?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 54
B = 126
What to be found:
find the lcm of 54 and 126
step 2 Find the prime factors of 54 and 126:
Prime factors of 54 = 2 x 3 x 3 x 3
Prime factors of 126 = 2 x 3 x 3 x 7
step 3 Identify the repeated and non-repeated prime factors of 54 and 126:
{2, 3, 3} are the most repeated factors and {3 x 7} are the non-repeated factors of 54 and 126.
step 4 Find the product of repeated and non-repeated prime factors of 54 and 126:
= 2 x 3 x 3 x 3 x 7
= 378
lcm(54 and 126) = 378
Hence,
lcm of 54 and 126 is 378
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 54 and 126.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 54 and 126
What to be found:
lcm (54, 126) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
54 and 126
step 3 Choose the divisor which divides each or most of the given integers (54 and 126), 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 54 and 126 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 54 | 126 |
| 3 | 27 | 63 |
| 3 | 9 | 21 |
| 3 | 3 | 7 |
| 7 | 1 | 7 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 54 and 126:
= 2 x 3 x 3 x 3 x 7
= 378
LCM(54, 126) = 378
The LCM of two numbers 54 and 126 is 378