LCM of 9 and 204
612 is the LCM of 9 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 9 and 204, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 9 and 204?
lcm (9 204) = (?)
9 => 3 x 3
204 => 2 x 2 x 3 x 17
= 3 x 3 x 2 x 2 x 17
= 612
lcm (9 and 204) = 612
612 is the LCM of 9 and 204.
where,
9 is a positive integer,
204 is a positive integer,
612 is the LCM of 9 and 204,
{3} in {3 x 3, 2 x 2 x 3 x 17} is the common factors of 9 and 204,
{3 x 2 x 2 x 17} in {3 x 3, 2 x 2 x 3 x 17} are the uncommon factors of 9 and 204.
Use in Mathematics: LCM of 9 and 204
The below are some of the mathematical applications where lcm of 9 and 204 can be used:
- to find the least number which is exactly divisible by 9 and 204.
- to find the common denominator for two fractions having 9 and 204 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 9 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 9 seconds and bell B tolls at 204 seconds repeatedly. The answer is that all bells A and B toll together at 612 seconds for the first time, at 1224 seconds for the second time, at 1836 seconds for the third time and so on.
Important Notes: 9 and 204 lcm
The below are the important notes to be remembered while solving the lcm of 9 and 204:
- The common prime factors and the remaining prime factors of 9 and 204 should be multiplied to find the least common multiple of 9 and 204, when solving lcm by using prime factors method.
- The results of lcm of 9 and 204, and the lcm of 204 and 9 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 9 and 204?
The below solved example with step by step work shows how to find what is the lcm of 9 and 204 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 9 and 204?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 9
B = 204
What to be found:
find the lcm of 9 and 204
step 2 Find the prime factors of 9 and 204:
Prime factors of 9 = 3 x 3
Prime factors of 204 = 2 x 2 x 3 x 17
step 3 Identify the repeated and non-repeated prime factors of 9 and 204:
{3} is the most repeated factor and {3 x 2 x 2 x 17} are the non-repeated factors of 9 and 204.
step 4 Find the product of repeated and non-repeated prime factors of 9 and 204:
= 3 x 3 x 2 x 2 x 17
= 612
lcm(9 and 204) = 612
Hence,
lcm of 9 and 204 is 612
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 9 and 204.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 9 and 204
What to be found:
lcm (9, 204) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
9 and 204
step 3 Choose the divisor which divides each or most of the given integers (9 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 9 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 | 9 | 204 |
| 2 | 9 | 102 |
| 3 | 9 | 51 |
| 3 | 3 | 17 |
| 17 | 1 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 9 and 204:
= 2 x 2 x 3 x 3 x 17
= 612
LCM(9, 204) = 612
The LCM of two numbers 9 and 204 is 612