LCM of 216 and 349
75384 is the LCM of 216 and 349. 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 216 and 349, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 216 and 349?
lcm (216 349) = (?)
216 => 2 x 2 x 2 x 3 x 3 x 3
349 => 349
= 2 x 2 x 2 x 3 x 3 x 3 x 349
= 75384
lcm (216 and 349) = 75384
75384 is the LCM of 216 and 349.
where,
216 is a positive integer,
349 is a positive integer,
75384 is the LCM of 216 and 349,
There is no common factors of 216 and 349 in {2 x 2 x 2 x 3 x 3 x 3, 349},
{2 x 2 x 2 x 3 x 3 x 3 x 349} in {2 x 2 x 2 x 3 x 3 x 3, 349} are the uncommon factors of 216 and 349.
Use in Mathematics: LCM of 216 and 349
The below are some of the mathematical applications where lcm of 216 and 349 can be used:
- to find the least number which is exactly divisible by 216 and 349.
- to find the common denominator for two fractions having 216 and 349 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 216 and 349 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 216 seconds and bell B tolls at 349 seconds repeatedly. The answer is that all bells A and B toll together at 75384 seconds for the first time, at 150768 seconds for the second time, at 226152 seconds for the third time and so on.
Important Notes: 216 and 349 lcm
The below are the important notes to be remembered while solving the lcm of 216 and 349:
- The common prime factors and the remaining prime factors of 216 and 349 should be multiplied to find the least common multiple of 216 and 349, when solving lcm by using prime factors method.
- The results of lcm of 216 and 349, and the lcm of 349 and 216 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 216 and 349?
The below solved example with step by step work shows how to find what is the lcm of 216 and 349 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 216 and 349?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 216
B = 349
What to be found:
find the lcm of 216 and 349
step 2 Find the prime factors of 216 and 349:
Prime factors of 216 = 2 x 2 x 2 x 3 x 3 x 3
Prime factors of 349 = 349
step 3Identify the repeated and non-repeated prime factors of 216 and 349:
Since there is no common factors between 216 and 349, multiplying the given numbers directly provides the LCM of
216 and 349.
= 216 x 349
= 75384
lcm(216 and 349) = 75384
Hence,
lcm of 216 and 349 is 75384
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 216 and 349.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 216 and 349
What to be found:
lcm (216, 349) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
216 and 349
step 3 Choose the divisor which divides each or most of the given integers (216 and 349), 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 216 and 349 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 216 | 349 |
| 2 | 108 | 349 |
| 2 | 54 | 349 |
| 3 | 27 | 349 |
| 3 | 9 | 349 |
| 3 | 3 | 349 |
| 349 | 1 | 349 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 216 and 349:
= 2 x 2 x 2 x 3 x 3 x 3 x 349
= 75384
LCM(216, 349) = 75384
The LCM of two numbers 216 and 349 is 75384