LCM of 99 and 204
6732 is the LCM of 99 and 204. 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 99 and 204, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 99 and 204?
lcm (99 204) = (?)
99 => 3 x 3 x 11
204 => 2 x 2 x 3 x 17
= 3 x 3 x 11 x 2 x 2 x 17
= 6732
lcm (99 and 204) = 6732
6732 is the LCM of 99 and 204.
where,
99 is a positive integer,
204 is a positive integer,
6732 is the LCM of 99 and 204,
{3} in {3 x 3 x 11, 2 x 2 x 3 x 17} is the common factors of 99 and 204,
{3 x 11 x 2 x 2 x 17} in {3 x 3 x 11, 2 x 2 x 3 x 17} are the uncommon factors of 99 and 204.
Use in Mathematics: LCM of 99 and 204
The below are some of the mathematical applications where lcm of 99 and 204 can be used:
- to find the least number which is exactly divisible by 99 and 204.
- to find the common denominator for two fractions having 99 and 204 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 99 and 204 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 99 seconds and bell B tolls at 204 seconds repeatedly. The answer is that all bells A and B toll together at 6732 seconds for the first time, at 13464 seconds for the second time, at 20196 seconds for the third time and so on.
Important Notes: 99 and 204 lcm
The below are the important notes to be remembered while solving the lcm of 99 and 204:
- The common prime factors and the remaining prime factors of 99 and 204 should be multiplied to find the least common multiple of 99 and 204, when solving lcm by using prime factors method.
- The results of lcm of 99 and 204, and the lcm of 204 and 99 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 99 and 204?
The below solved example with step by step work shows how to find what is the lcm of 99 and 204 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 99 and 204?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 99
B = 204
What to be found:
find the lcm of 99 and 204
step 2 Find the prime factors of 99 and 204:
Prime factors of 99 = 3 x 3 x 11
Prime factors of 204 = 2 x 2 x 3 x 17
step 3 Identify the repeated and non-repeated prime factors of 99 and 204:
{3} is the most repeated factor and {3 x 11 x 2 x 2 x 17} are the non-repeated factors of 99 and 204.
step 4 Find the product of repeated and non-repeated prime factors of 99 and 204:
= 3 x 3 x 11 x 2 x 2 x 17
= 6732
lcm(99 and 204) = 6732
Hence,
lcm of 99 and 204 is 6732
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 99 and 204.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 99 and 204
What to be found:
lcm (99, 204) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
99 and 204
step 3 Choose the divisor which divides each or most of the given integers (99 and 204), 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 99 and 204 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 99 | 204 |
| 2 | 99 | 102 |
| 3 | 99 | 51 |
| 3 | 33 | 17 |
| 11 | 11 | 17 |
| 17 | 1 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 99 and 204:
= 2 x 2 x 3 x 3 x 11 x 17
= 6732
LCM(99, 204) = 6732
The LCM of two numbers 99 and 204 is 6732