LCM of 216 and 320
8640 is the LCM of 216 and 320. 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 320, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 216 and 320?
lcm (216 320) = (?)
216 => 2 x 2 x 2 x 3 x 3 x 3
320 => 2 x 2 x 2 x 2 x 2 x 2 x 5
= 2 x 2 x 2 x 3 x 3 x 3 x 2 x 2 x 2 x 5
= 8640
lcm (216 and 320) = 8640
8640 is the LCM of 216 and 320.
where,
216 is a positive integer,
320 is a positive integer,
8640 is the LCM of 216 and 320,
{2 x 2 x 2} in {2 x 2 x 2 x 3 x 3 x 3, 2 x 2 x 2 x 2 x 2 x 2 x 5} are the common factors of 216 and 320,
{3 x 3 x 3 x 2 x 2 x 2 x 5} in {2 x 2 x 2 x 3 x 3 x 3, 2 x 2 x 2 x 2 x 2 x 2 x 5} are the uncommon factors of 216 and 320.
Use in Mathematics: LCM of 216 and 320
The below are some of the mathematical applications where lcm of 216 and 320 can be used:
- to find the least number which is exactly divisible by 216 and 320.
- to find the common denominator for two fractions having 216 and 320 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 216 and 320 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 320 seconds repeatedly. The answer is that all bells A and B toll together at 8640 seconds for the first time, at 17280 seconds for the second time, at 25920 seconds for the third time and so on.
Important Notes: 216 and 320 lcm
The below are the important notes to be remembered while solving the lcm of 216 and 320:
- The common prime factors and the remaining prime factors of 216 and 320 should be multiplied to find the least common multiple of 216 and 320, when solving lcm by using prime factors method.
- The results of lcm of 216 and 320, and the lcm of 320 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 320?
The below solved example with step by step work shows how to find what is the lcm of 216 and 320 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 216 and 320?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 216
B = 320
What to be found:
find the lcm of 216 and 320
step 2 Find the prime factors of 216 and 320:
Prime factors of 216 = 2 x 2 x 2 x 3 x 3 x 3
Prime factors of 320 = 2 x 2 x 2 x 2 x 2 x 2 x 5
step 3 Identify the repeated and non-repeated prime factors of 216 and 320:
{2, 2, 2} are the most repeated factors and {3 x 3 x 3 x 2 x 2 x 2 x 5} are the non-repeated factors of 216 and 320.
step 4 Find the product of repeated and non-repeated prime factors of 216 and 320:
= 2 x 2 x 2 x 3 x 3 x 3 x 2 x 2 x 2 x 5
= 8640
lcm(216 and 320) = 8640
Hence,
lcm of 216 and 320 is 8640
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 216 and 320.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 216 and 320
What to be found:
lcm (216, 320) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
216 and 320
step 3 Choose the divisor which divides each or most of the given integers (216 and 320), 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 320 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 216 | 320 |
| 2 | 108 | 160 |
| 2 | 54 | 80 |
| 2 | 27 | 40 |
| 2 | 27 | 20 |
| 2 | 27 | 10 |
| 3 | 27 | 5 |
| 3 | 9 | 5 |
| 3 | 3 | 5 |
| 5 | 1 | 5 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 216 and 320:
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5
= 8640
LCM(216, 320) = 8640
The LCM of two numbers 216 and 320 is 8640