LCM of 84 and 93
2604 is the LCM of 84 and 93. 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 93, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 84 and 93?
lcm (84 93) = (?)
84 => 2 x 2 x 3 x 7
93 => 3 x 31
= 3 x 2 x 2 x 7 x 31
= 2604
lcm (84 and 93) = 2604
2604 is the LCM of 84 and 93.
where,
84 is a positive integer,
93 is a positive integer,
2604 is the LCM of 84 and 93,
{3} in {2 x 2 x 3 x 7, 3 x 31} is the common factors of 84 and 93,
{2 x 2 x 7 x 31} in {2 x 2 x 3 x 7, 3 x 31} are the uncommon factors of 84 and 93.
Use in Mathematics: LCM of 84 and 93
The below are some of the mathematical applications where lcm of 84 and 93 can be used:
- to find the least number which is exactly divisible by 84 and 93.
- to find the common denominator for two fractions having 84 and 93 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 84 and 93 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 93 seconds repeatedly. The answer is that all bells A and B toll together at 2604 seconds for the first time, at 5208 seconds for the second time, at 7812 seconds for the third time and so on.
Important Notes: 84 and 93 lcm
The below are the important notes to be remembered while solving the lcm of 84 and 93:
- The common prime factors and the remaining prime factors of 84 and 93 should be multiplied to find the least common multiple of 84 and 93, when solving lcm by using prime factors method.
- The results of lcm of 84 and 93, and the lcm of 93 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 93?
The below solved example with step by step work shows how to find what is the lcm of 84 and 93 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 84 and 93?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 84
B = 93
What to be found:
find the lcm of 84 and 93
step 2 Find the prime factors of 84 and 93:
Prime factors of 84 = 2 x 2 x 3 x 7
Prime factors of 93 = 3 x 31
step 3 Identify the repeated and non-repeated prime factors of 84 and 93:
{3} is the most repeated factor and {2 x 2 x 7 x 31} are the non-repeated factors of 84 and 93.
step 4 Find the product of repeated and non-repeated prime factors of 84 and 93:
= 3 x 2 x 2 x 7 x 31
= 2604
lcm(84 and 93) = 2604
Hence,
lcm of 84 and 93 is 2604
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 84 and 93.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 84 and 93
What to be found:
lcm (84, 93) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
84 and 93
step 3 Choose the divisor which divides each or most of the given integers (84 and 93), 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 93 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 84 | 93 |
| 2 | 42 | 93 |
| 3 | 21 | 93 |
| 7 | 7 | 31 |
| 31 | 1 | 31 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 84 and 93:
= 2 x 2 x 3 x 7 x 31
= 2604
LCM(84, 93) = 2604
The LCM of two numbers 84 and 93 is 2604