LCM of 31 and 292
9052 is the LCM of 31 and 292. 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 31 and 292, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 31 and 292?
lcm (31 292) = (?)
31 => 31
292 => 2 x 2 x 73
= 31 x 2 x 2 x 73
= 9052
lcm (31 and 292) = 9052
9052 is the LCM of 31 and 292.
where,
31 is a positive integer,
292 is a positive integer,
9052 is the LCM of 31 and 292,
There is no common factors of 31 and 292 in {31, 2 x 2 x 73},
{31 x 2 x 2 x 73} in {31, 2 x 2 x 73} are the uncommon factors of 31 and 292.
Use in Mathematics: LCM of 31 and 292
The below are some of the mathematical applications where lcm of 31 and 292 can be used:
- to find the least number which is exactly divisible by 31 and 292.
- to find the common denominator for two fractions having 31 and 292 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 31 and 292 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 31 seconds and bell B tolls at 292 seconds repeatedly. The answer is that all bells A and B toll together at 9052 seconds for the first time, at 18104 seconds for the second time, at 27156 seconds for the third time and so on.
Important Notes: 31 and 292 lcm
The below are the important notes to be remembered while solving the lcm of 31 and 292:
- The common prime factors and the remaining prime factors of 31 and 292 should be multiplied to find the least common multiple of 31 and 292, when solving lcm by using prime factors method.
- The results of lcm of 31 and 292, and the lcm of 292 and 31 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 31 and 292?
The below solved example with step by step work shows how to find what is the lcm of 31 and 292 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 31 and 292?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 31
B = 292
What to be found:
find the lcm of 31 and 292
step 2 Find the prime factors of 31 and 292:
Prime factors of 31 = 31
Prime factors of 292 = 2 x 2 x 73
step 3Identify the repeated and non-repeated prime factors of 31 and 292:
Since there is no common factors between 31 and 292, multiplying the given numbers directly provides the LCM of
31 and 292.
= 31 x 292
= 9052
lcm(31 and 292) = 9052
Hence,
lcm of 31 and 292 is 9052
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 31 and 292.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 31 and 292
What to be found:
lcm (31, 292) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
31 and 292
step 3 Choose the divisor which divides each or most of the given integers (31 and 292), 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 31 and 292 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 31 | 292 |
| 2 | 31 | 146 |
| 31 | 31 | 73 |
| 73 | 1 | 73 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 31 and 292:
= 2 x 2 x 31 x 73
= 9052
LCM(31, 292) = 9052
The LCM of two numbers 31 and 292 is 9052