LCM of 32 and 239
7648 is the LCM of 32 and 239. 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 32 and 239, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 32 and 239?
lcm (32 239) = (?)
32 => 2 x 2 x 2 x 2 x 2
239 => 239
= 2 x 2 x 2 x 2 x 2 x 239
= 7648
lcm (32 and 239) = 7648
7648 is the LCM of 32 and 239.
where,
32 is a positive integer,
239 is a positive integer,
7648 is the LCM of 32 and 239,
There is no common factors of 32 and 239 in {2 x 2 x 2 x 2 x 2, 239},
{2 x 2 x 2 x 2 x 2 x 239} in {2 x 2 x 2 x 2 x 2, 239} are the uncommon factors of 32 and 239.
Use in Mathematics: LCM of 32 and 239
The below are some of the mathematical applications where lcm of 32 and 239 can be used:
- to find the least number which is exactly divisible by 32 and 239.
- to find the common denominator for two fractions having 32 and 239 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 32 and 239 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 32 seconds and bell B tolls at 239 seconds repeatedly. The answer is that all bells A and B toll together at 7648 seconds for the first time, at 15296 seconds for the second time, at 22944 seconds for the third time and so on.
Important Notes: 32 and 239 lcm
The below are the important notes to be remembered while solving the lcm of 32 and 239:
- The common prime factors and the remaining prime factors of 32 and 239 should be multiplied to find the least common multiple of 32 and 239, when solving lcm by using prime factors method.
- The results of lcm of 32 and 239, and the lcm of 239 and 32 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 32 and 239?
The below solved example with step by step work shows how to find what is the lcm of 32 and 239 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 32 and 239?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 32
B = 239
What to be found:
find the lcm of 32 and 239
step 2 Find the prime factors of 32 and 239:
Prime factors of 32 = 2 x 2 x 2 x 2 x 2
Prime factors of 239 = 239
step 3Identify the repeated and non-repeated prime factors of 32 and 239:
Since there is no common factors between 32 and 239, multiplying the given numbers directly provides the LCM of
32 and 239.
= 32 x 239
= 7648
lcm(32 and 239) = 7648
Hence,
lcm of 32 and 239 is 7648
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 32 and 239.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 32 and 239
What to be found:
lcm (32, 239) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
32 and 239
step 3 Choose the divisor which divides each or most of the given integers (32 and 239), 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 32 and 239 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 32 | 239 |
| 2 | 16 | 239 |
| 2 | 8 | 239 |
| 2 | 4 | 239 |
| 2 | 2 | 239 |
| 239 | 1 | 239 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 32 and 239:
= 2 x 2 x 2 x 2 x 2 x 239
= 7648
LCM(32, 239) = 7648
The LCM of two numbers 32 and 239 is 7648