LCM of 216 and 350
37800 is the LCM of 216 and 350. 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 350, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 216 and 350?
lcm (216 350) = (?)
216 => 2 x 2 x 2 x 3 x 3 x 3
350 => 2 x 5 x 5 x 7
= 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 7
= 37800
lcm (216 and 350) = 37800
37800 is the LCM of 216 and 350.
where,
216 is a positive integer,
350 is a positive integer,
37800 is the LCM of 216 and 350,
{2} in {2 x 2 x 2 x 3 x 3 x 3, 2 x 5 x 5 x 7} is the common factors of 216 and 350,
{2 x 2 x 3 x 3 x 3 x 5 x 5 x 7} in {2 x 2 x 2 x 3 x 3 x 3, 2 x 5 x 5 x 7} are the uncommon factors of 216 and 350.
Use in Mathematics: LCM of 216 and 350
The below are some of the mathematical applications where lcm of 216 and 350 can be used:
- to find the least number which is exactly divisible by 216 and 350.
- to find the common denominator for two fractions having 216 and 350 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 216 and 350 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 350 seconds repeatedly. The answer is that all bells A and B toll together at 37800 seconds for the first time, at 75600 seconds for the second time, at 113400 seconds for the third time and so on.
Important Notes: 216 and 350 lcm
The below are the important notes to be remembered while solving the lcm of 216 and 350:
- The common prime factors and the remaining prime factors of 216 and 350 should be multiplied to find the least common multiple of 216 and 350, when solving lcm by using prime factors method.
- The results of lcm of 216 and 350, and the lcm of 350 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 350?
The below solved example with step by step work shows how to find what is the lcm of 216 and 350 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 216 and 350?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 216
B = 350
What to be found:
find the lcm of 216 and 350
step 2 Find the prime factors of 216 and 350:
Prime factors of 216 = 2 x 2 x 2 x 3 x 3 x 3
Prime factors of 350 = 2 x 5 x 5 x 7
step 3 Identify the repeated and non-repeated prime factors of 216 and 350:
{2} is the most repeated factor and {2 x 2 x 3 x 3 x 3 x 5 x 5 x 7} are the non-repeated factors of 216 and 350.
step 4 Find the product of repeated and non-repeated prime factors of 216 and 350:
= 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 7
= 37800
lcm(216 and 350) = 37800
Hence,
lcm of 216 and 350 is 37800
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 216 and 350.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 216 and 350
What to be found:
lcm (216, 350) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
216 and 350
step 3 Choose the divisor which divides each or most of the given integers (216 and 350), 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 350 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 216 | 350 |
| 2 | 108 | 175 |
| 2 | 54 | 175 |
| 3 | 27 | 175 |
| 3 | 9 | 175 |
| 3 | 3 | 175 |
| 5 | 1 | 175 |
| 5 | 1 | 35 |
| 7 | 1 | 7 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 216 and 350:
= 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 7
= 37800
LCM(216, 350) = 37800
The LCM of two numbers 216 and 350 is 37800