LCM of 6 and 274
822 is the LCM of 6 and 274. 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 274, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 6 and 274?
lcm (6 274) = (?)
6 => 2 x 3
274 => 2 x 137
= 2 x 3 x 137
= 822
lcm (6 and 274) = 822
822 is the LCM of 6 and 274.
where,
6 is a positive integer,
274 is a positive integer,
822 is the LCM of 6 and 274,
{2} in {2 x 3, 2 x 137} is the common factors of 6 and 274,
{3 x 137} in {2 x 3, 2 x 137} are the uncommon factors of 6 and 274.
Use in Mathematics: LCM of 6 and 274
The below are some of the mathematical applications where lcm of 6 and 274 can be used:
- to find the least number which is exactly divisible by 6 and 274.
- to find the common denominator for two fractions having 6 and 274 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 6 and 274 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 274 seconds repeatedly. The answer is that all bells A and B toll together at 822 seconds for the first time, at 1644 seconds for the second time, at 2466 seconds for the third time and so on.
Important Notes: 6 and 274 lcm
The below are the important notes to be remembered while solving the lcm of 6 and 274:
- The common prime factors and the remaining prime factors of 6 and 274 should be multiplied to find the least common multiple of 6 and 274, when solving lcm by using prime factors method.
- The results of lcm of 6 and 274, and the lcm of 274 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 274?
The below solved example with step by step work shows how to find what is the lcm of 6 and 274 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 6 and 274?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 6
B = 274
What to be found:
find the lcm of 6 and 274
step 2 Find the prime factors of 6 and 274:
Prime factors of 6 = 2 x 3
Prime factors of 274 = 2 x 137
step 3 Identify the repeated and non-repeated prime factors of 6 and 274:
{2} is the most repeated factor and {3 x 137} are the non-repeated factors of 6 and 274.
step 4 Find the product of repeated and non-repeated prime factors of 6 and 274:
= 2 x 3 x 137
= 822
lcm(6 and 274) = 822
Hence,
lcm of 6 and 274 is 822
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 6 and 274.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 6 and 274
What to be found:
lcm (6, 274) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
6 and 274
step 3 Choose the divisor which divides each or most of the given integers (6 and 274), 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 274 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 6 | 274 |
| 3 | 3 | 137 |
| 137 | 1 | 137 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 6 and 274:
= 2 x 3 x 137
= 822
LCM(6, 274) = 822
The LCM of two numbers 6 and 274 is 822