LCM of 126 and 183
7686 is the LCM of 126 and 183. 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 183, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 126 and 183?
lcm (126 183) = (?)
126 => 2 x 3 x 3 x 7
183 => 3 x 61
= 3 x 2 x 3 x 7 x 61
= 7686
lcm (126 and 183) = 7686
7686 is the LCM of 126 and 183.
where,
126 is a positive integer,
183 is a positive integer,
7686 is the LCM of 126 and 183,
{3} in {2 x 3 x 3 x 7, 3 x 61} is the common factors of 126 and 183,
{2 x 3 x 7 x 61} in {2 x 3 x 3 x 7, 3 x 61} are the uncommon factors of 126 and 183.
Use in Mathematics: LCM of 126 and 183
The below are some of the mathematical applications where lcm of 126 and 183 can be used:
- to find the least number which is exactly divisible by 126 and 183.
- to find the common denominator for two fractions having 126 and 183 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 126 and 183 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 183 seconds repeatedly. The answer is that all bells A and B toll together at 7686 seconds for the first time, at 15372 seconds for the second time, at 23058 seconds for the third time and so on.
Important Notes: 126 and 183 lcm
The below are the important notes to be remembered while solving the lcm of 126 and 183:
- The common prime factors and the remaining prime factors of 126 and 183 should be multiplied to find the least common multiple of 126 and 183, when solving lcm by using prime factors method.
- The results of lcm of 126 and 183, and the lcm of 183 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 183?
The below solved example with step by step work shows how to find what is the lcm of 126 and 183 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 126 and 183?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 126
B = 183
What to be found:
find the lcm of 126 and 183
step 2 Find the prime factors of 126 and 183:
Prime factors of 126 = 2 x 3 x 3 x 7
Prime factors of 183 = 3 x 61
step 3 Identify the repeated and non-repeated prime factors of 126 and 183:
{3} is the most repeated factor and {2 x 3 x 7 x 61} are the non-repeated factors of 126 and 183.
step 4 Find the product of repeated and non-repeated prime factors of 126 and 183:
= 3 x 2 x 3 x 7 x 61
= 7686
lcm(126 and 183) = 7686
Hence,
lcm of 126 and 183 is 7686
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 126 and 183.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 126 and 183
What to be found:
lcm (126, 183) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
126 and 183
step 3 Choose the divisor which divides each or most of the given integers (126 and 183), 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 183 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 126 | 183 |
| 3 | 63 | 183 |
| 3 | 21 | 61 |
| 7 | 7 | 61 |
| 61 | 1 | 61 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 126 and 183:
= 2 x 3 x 3 x 7 x 61
= 7686
LCM(126, 183) = 7686
The LCM of two numbers 126 and 183 is 7686