LCM of 6 and 117
234 is the LCM of 6 and 117. 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 6 and 117, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 6 and 117?
lcm (6 117) = (?)
6 => 2 x 3
117 => 3 x 3 x 13
= 3 x 2 x 3 x 13
= 234
lcm (6 and 117) = 234
234 is the LCM of 6 and 117.
where,
6 is a positive integer,
117 is a positive integer,
234 is the LCM of 6 and 117,
{3} in {2 x 3, 3 x 3 x 13} is the common factors of 6 and 117,
{2 x 3 x 13} in {2 x 3, 3 x 3 x 13} are the uncommon factors of 6 and 117.
Use in Mathematics: LCM of 6 and 117
The below are some of the mathematical applications where lcm of 6 and 117 can be used:
- to find the least number which is exactly divisible by 6 and 117.
- to find the common denominator for two fractions having 6 and 117 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 6 and 117 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 6 seconds and bell B tolls at 117 seconds repeatedly. The answer is that all bells A and B toll together at 234 seconds for the first time, at 468 seconds for the second time, at 702 seconds for the third time and so on.
Important Notes: 6 and 117 lcm
The below are the important notes to be remembered while solving the lcm of 6 and 117:
- The common prime factors and the remaining prime factors of 6 and 117 should be multiplied to find the least common multiple of 6 and 117, when solving lcm by using prime factors method.
- The results of lcm of 6 and 117, and the lcm of 117 and 6 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 6 and 117?
The below solved example with step by step work shows how to find what is the lcm of 6 and 117 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 6 and 117?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 6
B = 117
What to be found:
find the lcm of 6 and 117
step 2 Find the prime factors of 6 and 117:
Prime factors of 6 = 2 x 3
Prime factors of 117 = 3 x 3 x 13
step 3 Identify the repeated and non-repeated prime factors of 6 and 117:
{3} is the most repeated factor and {2 x 3 x 13} are the non-repeated factors of 6 and 117.
step 4 Find the product of repeated and non-repeated prime factors of 6 and 117:
= 3 x 2 x 3 x 13
= 234
lcm(6 and 117) = 234
Hence,
lcm of 6 and 117 is 234
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 6 and 117.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 6 and 117
What to be found:
lcm (6, 117) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
6 and 117
step 3 Choose the divisor which divides each or most of the given integers (6 and 117), 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 6 and 117 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 6 | 117 |
| 3 | 3 | 117 |
| 3 | 1 | 39 |
| 13 | 1 | 13 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 6 and 117:
= 2 x 3 x 3 x 13
= 234
LCM(6, 117) = 234
The LCM of two numbers 6 and 117 is 234