LCM of 283 and 342
96786 is the LCM of 283 and 342. 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 283 and 342, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 283 and 342?
lcm (283 342) = (?)
283 => 283
342 => 2 x 3 x 3 x 19
= 283 x 2 x 3 x 3 x 19
= 96786
lcm (283 and 342) = 96786
96786 is the LCM of 283 and 342.
where,
283 is a positive integer,
342 is a positive integer,
96786 is the LCM of 283 and 342,
There is no common factors of 283 and 342 in {283, 2 x 3 x 3 x 19},
{283 x 2 x 3 x 3 x 19} in {283, 2 x 3 x 3 x 19} are the uncommon factors of 283 and 342.
Use in Mathematics: LCM of 283 and 342
The below are some of the mathematical applications where lcm of 283 and 342 can be used:
- to find the least number which is exactly divisible by 283 and 342.
- to find the common denominator for two fractions having 283 and 342 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 283 and 342 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 283 seconds and bell B tolls at 342 seconds repeatedly. The answer is that all bells A and B toll together at 96786 seconds for the first time, at 193572 seconds for the second time, at 290358 seconds for the third time and so on.
Important Notes: 283 and 342 lcm
The below are the important notes to be remembered while solving the lcm of 283 and 342:
- The common prime factors and the remaining prime factors of 283 and 342 should be multiplied to find the least common multiple of 283 and 342, when solving lcm by using prime factors method.
- The results of lcm of 283 and 342, and the lcm of 342 and 283 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 283 and 342?
The below solved example with step by step work shows how to find what is the lcm of 283 and 342 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 283 and 342?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 283
B = 342
What to be found:
find the lcm of 283 and 342
step 2 Find the prime factors of 283 and 342:
Prime factors of 283 = 283
Prime factors of 342 = 2 x 3 x 3 x 19
step 3Identify the repeated and non-repeated prime factors of 283 and 342:
Since there is no common factors between 283 and 342, multiplying the given numbers directly provides the LCM of
283 and 342.
= 283 x 342
= 96786
lcm(283 and 342) = 96786
Hence,
lcm of 283 and 342 is 96786
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 283 and 342.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 283 and 342
What to be found:
lcm (283, 342) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
283 and 342
step 3 Choose the divisor which divides each or most of the given integers (283 and 342), 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 283 and 342 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 283 | 342 |
| 3 | 283 | 171 |
| 3 | 283 | 57 |
| 19 | 283 | 19 |
| 283 | 283 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 283 and 342:
= 2 x 3 x 3 x 19 x 283
= 96786
LCM(283, 342) = 96786
The LCM of two numbers 283 and 342 is 96786