LCM of 84 and 258
3612 is the LCM of 84 and 258. 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 84 and 258, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 84 and 258?
lcm (84 258) = (?)
84 => 2 x 2 x 3 x 7
258 => 2 x 3 x 43
= 2 x 3 x 2 x 7 x 43
= 3612
lcm (84 and 258) = 3612
3612 is the LCM of 84 and 258.
where,
84 is a positive integer,
258 is a positive integer,
3612 is the LCM of 84 and 258,
{2 x 3} in {2 x 2 x 3 x 7, 2 x 3 x 43} are the common factors of 84 and 258,
{2 x 7 x 43} in {2 x 2 x 3 x 7, 2 x 3 x 43} are the uncommon factors of 84 and 258.
Use in Mathematics: LCM of 84 and 258
The below are some of the mathematical applications where lcm of 84 and 258 can be used:
- to find the least number which is exactly divisible by 84 and 258.
- to find the common denominator for two fractions having 84 and 258 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 84 and 258 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 84 seconds and bell B tolls at 258 seconds repeatedly. The answer is that all bells A and B toll together at 3612 seconds for the first time, at 7224 seconds for the second time, at 10836 seconds for the third time and so on.
Important Notes: 84 and 258 lcm
The below are the important notes to be remembered while solving the lcm of 84 and 258:
- The common prime factors and the remaining prime factors of 84 and 258 should be multiplied to find the least common multiple of 84 and 258, when solving lcm by using prime factors method.
- The results of lcm of 84 and 258, and the lcm of 258 and 84 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 84 and 258?
The below solved example with step by step work shows how to find what is the lcm of 84 and 258 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 84 and 258?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 84
B = 258
What to be found:
find the lcm of 84 and 258
step 2 Find the prime factors of 84 and 258:
Prime factors of 84 = 2 x 2 x 3 x 7
Prime factors of 258 = 2 x 3 x 43
step 3 Identify the repeated and non-repeated prime factors of 84 and 258:
{2, 3} are the most repeated factors and {2 x 7 x 43} are the non-repeated factors of 84 and 258.
step 4 Find the product of repeated and non-repeated prime factors of 84 and 258:
= 2 x 3 x 2 x 7 x 43
= 3612
lcm(84 and 258) = 3612
Hence,
lcm of 84 and 258 is 3612
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 84 and 258.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 84 and 258
What to be found:
lcm (84, 258) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
84 and 258
step 3 Choose the divisor which divides each or most of the given integers (84 and 258), 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 84 and 258 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 84 | 258 |
| 2 | 42 | 129 |
| 3 | 21 | 129 |
| 7 | 7 | 43 |
| 43 | 1 | 43 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 84 and 258:
= 2 x 2 x 3 x 7 x 43
= 3612
LCM(84, 258) = 3612
The LCM of two numbers 84 and 258 is 3612