84 and 146 LCM
LCM of 84 and 146 is equal to 6132. The comprehensive work provides more insight of how to find what is the lcm of 84 and 146 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 84 and 146?
lcm (84 146) = (?)
84 => 2 x 2 x 3 x 7
146 => 2 x 73
= 2 x 2 x 3 x 7 x 73
= 6132
lcm (84 and 146) = 6132
6132 is the lcm of 84 and 146.
where,
84 is a positive integer,
146 is a positive integer,
6132 is the lcm of 84 and 146,
{2} in {2 x 2 x 3 x 7, 2 x 73} is the common factors of 84 and 146,
{2 x 3 x 7 x 73} in {2 x 2 x 3 x 7, 2 x 73} are the uncommon factors of 84 and 146.
Use in Mathematics: LCM of 84 and 146
The below are some of the mathematical applications where lcm of 84 and 146 can be used:
- to find the least number which is exactly divisible by 84 and 146.
- to find the common denominator for two fractions having 84 and 146 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 84 and 146 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 146 seconds repeatedly. The answer is that all bells A and B toll together at 6132 seconds for the first time, at 12264 seconds for the second time, at 18396 seconds for the third time and so on.
Important Notes: 84 and 146 lcm
The below are the important notes to be remembered while solving the lcm of 84 and 146:
- The common prime factors and the remaining prime factors of 84 and 146 should be multiplied to find the least common multiple of 84 and 146, when solving lcm by using prime factors method.
- The results of lcm of 84 and 146, and the lcm of 146 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 146?
The below solved example with step by step work shows how to find what is the lcm of 84 and 146 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 84 and 146?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 84
B = 146
What to be found:
find the lcm of 84 and 146
step 2 Find the prime factors of 84 and 146:
Prime factors of 84 = 2 x 2 x 3 x 7
Prime factors of 146 = 2 x 73
step 3 Identify the repeated and non-repeated prime factors of 84 and 146:
{2} is the most repeated factor and {2 x 3 x 7 x 73} are the non-repeated factors of 84 and 146.
step 4 Find the product of repeated and non-repeated prime factors of 84 and 146:
= 2 x 2 x 3 x 7 x 73
= 6132
lcm(84 and 146) = 6132
Hence,
lcm of 84 and 146 is 6132
This special division method is the easiest way to understand the entire calculation of what is the lcm of 84 and 146.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 84 and 146
What to be found:
lcm (84, 146) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
84 and 146
step 3 Choose the divisor which divides each or most of the given integers (84 and 146), 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 146 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 84 | 146 |
| 2 | 42 | 73 |
| 3 | 21 | 73 |
| 7 | 7 | 73 |
| 73 | 1 | 73 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 84 and 146:
= 2 x 2 x 3 x 7 x 73
= 6132
LCM(84, 146) = 6132
The least common multiple for two numbers 84 and 146 is 6132