LCM of 219 and 324
23652 is the LCM of 219 and 324. 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 219 and 324, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 219 and 324?
lcm (219 324) = (?)
219 => 3 x 73
324 => 2 x 2 x 3 x 3 x 3 x 3
= 3 x 73 x 2 x 2 x 3 x 3 x 3
= 23652
lcm (219 and 324) = 23652
23652 is the LCM of 219 and 324.
where,
219 is a positive integer,
324 is a positive integer,
23652 is the LCM of 219 and 324,
{3} in {3 x 73, 2 x 2 x 3 x 3 x 3 x 3} is the common factors of 219 and 324,
{73 x 2 x 2 x 3 x 3 x 3} in {3 x 73, 2 x 2 x 3 x 3 x 3 x 3} are the uncommon factors of 219 and 324.
Use in Mathematics: LCM of 219 and 324
The below are some of the mathematical applications where lcm of 219 and 324 can be used:
- to find the least number which is exactly divisible by 219 and 324.
- to find the common denominator for two fractions having 219 and 324 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 219 and 324 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 219 seconds and bell B tolls at 324 seconds repeatedly. The answer is that all bells A and B toll together at 23652 seconds for the first time, at 47304 seconds for the second time, at 70956 seconds for the third time and so on.
Important Notes: 219 and 324 lcm
The below are the important notes to be remembered while solving the lcm of 219 and 324:
- The common prime factors and the remaining prime factors of 219 and 324 should be multiplied to find the least common multiple of 219 and 324, when solving lcm by using prime factors method.
- The results of lcm of 219 and 324, and the lcm of 324 and 219 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 219 and 324?
The below solved example with step by step work shows how to find what is the lcm of 219 and 324 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 219 and 324?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 219
B = 324
What to be found:
find the lcm of 219 and 324
step 2 Find the prime factors of 219 and 324:
Prime factors of 219 = 3 x 73
Prime factors of 324 = 2 x 2 x 3 x 3 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 219 and 324:
{3} is the most repeated factor and {73 x 2 x 2 x 3 x 3 x 3} are the non-repeated factors of 219 and 324.
step 4 Find the product of repeated and non-repeated prime factors of 219 and 324:
= 3 x 73 x 2 x 2 x 3 x 3 x 3
= 23652
lcm(219 and 324) = 23652
Hence,
lcm of 219 and 324 is 23652
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 219 and 324.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 219 and 324
What to be found:
lcm (219, 324) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
219 and 324
step 3 Choose the divisor which divides each or most of the given integers (219 and 324), 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 219 and 324 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 219 | 324 |
| 2 | 219 | 162 |
| 3 | 219 | 81 |
| 3 | 73 | 27 |
| 3 | 73 | 9 |
| 3 | 73 | 3 |
| 73 | 73 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 219 and 324:
= 2 x 2 x 3 x 3 x 3 x 3 x 73
= 23652
LCM(219, 324) = 23652
The LCM of two numbers 219 and 324 is 23652