LCM of 17 and 32
544 is the LCM of 17 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 17 and 32, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 17 and 32?
lcm (17 32) = (?)
17 => 17
32 => 2 x 2 x 2 x 2 x 2
= 17 x 2 x 2 x 2 x 2 x 2
= 544
lcm (17 and 32) = 544
544 is the LCM of 17 and 32.
where,
17 is a positive integer,
32 is a positive integer,
544 is the LCM of 17 and 32,
There is no common factors of 17 and 32 in {17, 2 x 2 x 2 x 2 x 2},
{17 x 2 x 2 x 2 x 2 x 2} in {17, 2 x 2 x 2 x 2 x 2} are the uncommon factors of 17 and 32.
Use in Mathematics: LCM of 17 and 32
The below are some of the mathematical applications where lcm of 17 and 32 can be used:
- to find the least number which is exactly divisible by 17 and 32.
- to find the common denominator for two fractions having 17 and 32 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 17 and 32 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 17 seconds and bell B tolls at 32 seconds repeatedly. The answer is that all bells A and B toll together at 544 seconds for the first time, at 1088 seconds for the second time, at 1632 seconds for the third time and so on.
Important Notes: 17 and 32 lcm
The below are the important notes to be remembered while solving the lcm of 17 and 32:
- The common prime factors and the remaining prime factors of 17 and 32 should be multiplied to find the least common multiple of 17 and 32, when solving lcm by using prime factors method.
- The results of lcm of 17 and 32, and the lcm of 32 and 17 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 17 and 32?
The below solved example with step by step work shows how to find what is the lcm of 17 and 32 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 17 and 32?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 17
B = 32
What to be found:
find the lcm of 17 and 32
step 2 Find the prime factors of 17 and 32:
Prime factors of 17 = 17
Prime factors of 32 = 2 x 2 x 2 x 2 x 2
step 3Identify the repeated and non-repeated prime factors of 17 and 32:
Since there is no common factors between 17 and 32, multiplying the given numbers directly provides the LCM of
17 and 32.
= 17 x 32
= 544
lcm(17 and 32) = 544
Hence,
lcm of 17 and 32 is 544
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 17 and 32.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 17 and 32
What to be found:
lcm (17, 32) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
17 and 32
step 3 Choose the divisor which divides each or most of the given integers (17 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 17 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 | 17 | 32 |
| 2 | 17 | 16 |
| 2 | 17 | 8 |
| 2 | 17 | 4 |
| 2 | 17 | 2 |
| 17 | 17 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 17 and 32:
= 2 x 2 x 2 x 2 x 2 x 17
= 544
LCM(17, 32) = 544
The LCM of two numbers 17 and 32 is 544