LCM of 108 and 248
6696 is the LCM of 108 and 248. 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 108 and 248, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 108 and 248?
lcm (108 248) = (?)
108 => 2 x 2 x 3 x 3 x 3
248 => 2 x 2 x 2 x 31
= 2 x 2 x 3 x 3 x 3 x 2 x 31
= 6696
lcm (108 and 248) = 6696
6696 is the LCM of 108 and 248.
where,
108 is a positive integer,
248 is a positive integer,
6696 is the LCM of 108 and 248,
{2 x 2} in {2 x 2 x 3 x 3 x 3, 2 x 2 x 2 x 31} are the common factors of 108 and 248,
{3 x 3 x 3 x 2 x 31} in {2 x 2 x 3 x 3 x 3, 2 x 2 x 2 x 31} are the uncommon factors of 108 and 248.
Use in Mathematics: LCM of 108 and 248
The below are some of the mathematical applications where lcm of 108 and 248 can be used:
- to find the least number which is exactly divisible by 108 and 248.
- to find the common denominator for two fractions having 108 and 248 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 108 and 248 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 108 seconds and bell B tolls at 248 seconds repeatedly. The answer is that all bells A and B toll together at 6696 seconds for the first time, at 13392 seconds for the second time, at 20088 seconds for the third time and so on.
Important Notes: 108 and 248 lcm
The below are the important notes to be remembered while solving the lcm of 108 and 248:
- The common prime factors and the remaining prime factors of 108 and 248 should be multiplied to find the least common multiple of 108 and 248, when solving lcm by using prime factors method.
- The results of lcm of 108 and 248, and the lcm of 248 and 108 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 108 and 248?
The below solved example with step by step work shows how to find what is the lcm of 108 and 248 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 108 and 248?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 108
B = 248
What to be found:
find the lcm of 108 and 248
step 2 Find the prime factors of 108 and 248:
Prime factors of 108 = 2 x 2 x 3 x 3 x 3
Prime factors of 248 = 2 x 2 x 2 x 31
step 3 Identify the repeated and non-repeated prime factors of 108 and 248:
{2, 2} are the most repeated factors and {3 x 3 x 3 x 2 x 31} are the non-repeated factors of 108 and 248.
step 4 Find the product of repeated and non-repeated prime factors of 108 and 248:
= 2 x 2 x 3 x 3 x 3 x 2 x 31
= 6696
lcm(108 and 248) = 6696
Hence,
lcm of 108 and 248 is 6696
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 108 and 248.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 108 and 248
What to be found:
lcm (108, 248) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
108 and 248
step 3 Choose the divisor which divides each or most of the given integers (108 and 248), 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 108 and 248 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 108 | 248 |
| 2 | 54 | 124 |
| 2 | 27 | 62 |
| 3 | 27 | 31 |
| 3 | 9 | 31 |
| 3 | 3 | 31 |
| 31 | 1 | 31 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 108 and 248:
= 2 x 2 x 2 x 3 x 3 x 3 x 31
= 6696
LCM(108, 248) = 6696
The LCM of two numbers 108 and 248 is 6696