LCM of 143 and 284
40612 is the LCM of 143 and 284. 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 143 and 284, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 143 and 284?
lcm (143 284) = (?)
143 => 11 x 13
284 => 2 x 2 x 71
= 11 x 13 x 2 x 2 x 71
= 40612
lcm (143 and 284) = 40612
40612 is the LCM of 143 and 284.
where,
143 is a positive integer,
284 is a positive integer,
40612 is the LCM of 143 and 284,
There is no common factors of 143 and 284 in {11 x 13, 2 x 2 x 71},
{11 x 13 x 2 x 2 x 71} in {11 x 13, 2 x 2 x 71} are the uncommon factors of 143 and 284.
Use in Mathematics: LCM of 143 and 284
The below are some of the mathematical applications where lcm of 143 and 284 can be used:
- to find the least number which is exactly divisible by 143 and 284.
- to find the common denominator for two fractions having 143 and 284 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 143 and 284 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 143 seconds and bell B tolls at 284 seconds repeatedly. The answer is that all bells A and B toll together at 40612 seconds for the first time, at 81224 seconds for the second time, at 121836 seconds for the third time and so on.
Important Notes: 143 and 284 lcm
The below are the important notes to be remembered while solving the lcm of 143 and 284:
- The common prime factors and the remaining prime factors of 143 and 284 should be multiplied to find the least common multiple of 143 and 284, when solving lcm by using prime factors method.
- The results of lcm of 143 and 284, and the lcm of 284 and 143 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 143 and 284?
The below solved example with step by step work shows how to find what is the lcm of 143 and 284 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 143 and 284?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 143
B = 284
What to be found:
find the lcm of 143 and 284
step 2 Find the prime factors of 143 and 284:
Prime factors of 143 = 11 x 13
Prime factors of 284 = 2 x 2 x 71
step 3Identify the repeated and non-repeated prime factors of 143 and 284:
Since there is no common factors between 143 and 284, multiplying the given numbers directly provides the LCM of
143 and 284.
= 143 x 284
= 40612
lcm(143 and 284) = 40612
Hence,
lcm of 143 and 284 is 40612
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 143 and 284.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 143 and 284
What to be found:
lcm (143, 284) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
143 and 284
step 3 Choose the divisor which divides each or most of the given integers (143 and 284), 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 143 and 284 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 143 | 284 |
| 2 | 143 | 142 |
| 11 | 143 | 71 |
| 13 | 13 | 71 |
| 71 | 1 | 71 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 143 and 284:
= 2 x 2 x 11 x 13 x 71
= 40612
LCM(143, 284) = 40612
The LCM of two numbers 143 and 284 is 40612