LCM of 3, 6 and 9
18 is the LCM of 3, 6 and 9. 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 3, 6 and 9, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 3, 6 and 9?
lcm (3 6 9) = (?)
3 => 3
6 => 2 x 3
9 => 3 x 3
= 3 x 2 x 3
= 18
lcm (3, 6 and 9) = 18
The LCM of 3, 6 and 9 is 18
where,
3 is a positive integer,
6 is a positive integer,
18 is the LCM of 3, 6 and 9,
{3} in {3, 2 x 3, 3 x 3} is the most repeated factors of 3, 6 and 9,
{2, 3} in {3, 2 x 3, 3 x 3} are the the other remaining factors of 3, 6 and 9.
Use in Mathematics: LCM of 3, 6 and 9
The below are some of the mathematical applications where lcm of 3, 6 and 9 can be used:
- to find the least number which is exactly divisible by 3, 6 and 9.
- to find the common denominators for the fractions having 3, 6 and 9 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 3, 6 and 9 helps to find the exact time when three similar and recurring 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 all the bells A, B and C toll together, if bell A tolls at 3 seconds, B tolls at 6 seconds and C tolls at 9 seconds repeatedly. The answer is that all bells A, B and C toll together at 18 seconds for the first time, at 36 seconds for the second time, at 54 seconds for the third time and so on.
Important Notes: 3, 6 and 9 lcm
The below are the important notes to be remembered while solving the lcm of 3, 6 and 9:
- The repeated and non-repeated prime factors of 3, 6 and 9 should be multiplied to find the least common multiple of 3, 6 and 9, when solving lcm by using prime factors method.
- The results of lcm of 3, 6 and 9 is identical even if we change the order of given numbers in the lcm calculation, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is LCM of 3, 6 and 9?
The below solved example with step by step work shows how to find what is the lcm of 3, 6 and 9 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 3, 6 and 9?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 3
B = 6
C = 9
What to be found:
Find lcm of 3, 6 and 9
step 2 Find the prime factors of 3, 6 and 9:
Prime factors of 3 = 3
Prime factors of 6 = 2 x 3
Prime factors of 9 = 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 3, 6 and 9:
{3} is the most repeated factor and {2, 3} are the non-repeated factors of 3, 6 and 9.
step 4 Find the product of repeated and non-repeated prime factors of 3, 6 and 9:
= 3 x 2 x 3
= 18
LCM(3, 6 and 9) = 18
Hence,
The Least Common Multiple of 3, 6 and 9 is 18
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 3, 6 and 9.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 3, 6 and 9
What to be found:
lcm (3, 6, 9) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
3, 6 and 9
step 3 Choose the divisor which divides each or most of the given integers (3, 6 and 9), 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 3, 6 and 9 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 3 | 6 | 9 |
| 3 | 3 | 3 | 9 |
| 3 | 1 | 1 | 3 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 3, 6 and 9:
= 2 x 3 x 3
= 18
LCM(3, 6, 9) = 18
The LCM of three numbers 3, 6 and 9 is 18