LCM of 6, 9 and 32
288 is the LCM of 6, 9 and 32. 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 6, 9 and 32, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 6, 9 and 32?
lcm (6 9 32) = (?)
6 => 2 x 3
9 => 3 x 3
32 => 2 x 2 x 2 x 2 x 2
= 2 x 3 x 3 x 2 x 2 x 2 x 2
= 288
lcm (6, 9 and 32) = 288
The LCM of 6, 9 and 32 is 288
where,
6 is a positive integer,
9 is a positive integer,
288 is the LCM of 6, 9 and 32,
{2, 3} in {2 x 3, 3 x 3, 2 x 2 x 2 x 2 x 2} are the most repeated factors of 6, 9 and 32,
{3, 2, 2, 2, 2} in {2 x 3, 3 x 3, 2 x 2 x 2 x 2 x 2} are the the other remaining factors of 6, 9 and 32.
Use in Mathematics: LCM of 6, 9 and 32
The below are some of the mathematical applications where lcm of 6, 9 and 32 can be used:
- to find the least number which is exactly divisible by 6, 9 and 32.
- to find the common denominators for the fractions having 6, 9 and 32 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 6, 9 and 32 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 6 seconds, B tolls at 9 seconds and C tolls at 32 seconds repeatedly. The answer is that all bells A, B and C toll together at 288 seconds for the first time, at 576 seconds for the second time, at 864 seconds for the third time and so on.
Important Notes: 6, 9 and 32 lcm
The below are the important notes to be remembered while solving the lcm of 6, 9 and 32:
- The repeated and non-repeated prime factors of 6, 9 and 32 should be multiplied to find the least common multiple of 6, 9 and 32, when solving lcm by using prime factors method.
- The results of lcm of 6, 9 and 32 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 6, 9 and 32?
The below solved example with step by step work shows how to find what is the lcm of 6, 9 and 32 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 6, 9 and 32?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 6
B = 9
C = 32
What to be found:
Find lcm of 6, 9 and 32
step 2 Find the prime factors of 6, 9 and 32:
Prime factors of 6 = 2 x 3
Prime factors of 9 = 3 x 3
Prime factors of 32 = 2 x 2 x 2 x 2 x 2
step 3 Identify the repeated and non-repeated prime factors of 6, 9 and 32:
{2, 3} are the most repeated factors and {3, 2, 2, 2, 2} are the non-repeated factors of 6, 9 and 32.
step 4 Find the product of repeated and non-repeated prime factors of 6, 9 and 32:
= 2 x 3 x 3 x 2 x 2 x 2 x 2
= 288
LCM(6, 9 and 32) = 288
Hence,
The Least Common Multiple of 6, 9 and 32 is 288
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 6, 9 and 32.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 6, 9 and 32
What to be found:
lcm (6, 9, 32) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
6, 9 and 32
step 3 Choose the divisor which divides each or most of the given integers (6, 9 and 32), 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 6, 9 and 32 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 6 | 9 | 32 |
| 2 | 3 | 9 | 16 |
| 2 | 3 | 9 | 8 |
| 2 | 3 | 9 | 4 |
| 2 | 3 | 9 | 2 |
| 3 | 3 | 9 | 1 |
| 3 | 1 | 3 | 1 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 6, 9 and 32:
= 2 x 2 x 2 x 2 x 2 x 3 x 3
= 288
LCM(6, 9, 32) = 288
The LCM of three numbers 6, 9 and 32 is 288