LCM of 105 and 208
21840 is the LCM of 105 and 208. 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 105 and 208, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 105 and 208?
lcm (105 208) = (?)
105 => 3 x 5 x 7
208 => 2 x 2 x 2 x 2 x 13
= 3 x 5 x 7 x 2 x 2 x 2 x 2 x 13
= 21840
lcm (105 and 208) = 21840
21840 is the LCM of 105 and 208.
where,
105 is a positive integer,
208 is a positive integer,
21840 is the LCM of 105 and 208,
There is no common factors of 105 and 208 in {3 x 5 x 7, 2 x 2 x 2 x 2 x 13},
{3 x 5 x 7 x 2 x 2 x 2 x 2 x 13} in {3 x 5 x 7, 2 x 2 x 2 x 2 x 13} are the uncommon factors of 105 and 208.
Use in Mathematics: LCM of 105 and 208
The below are some of the mathematical applications where lcm of 105 and 208 can be used:
- to find the least number which is exactly divisible by 105 and 208.
- to find the common denominator for two fractions having 105 and 208 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 105 and 208 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 105 seconds and bell B tolls at 208 seconds repeatedly. The answer is that all bells A and B toll together at 21840 seconds for the first time, at 43680 seconds for the second time, at 65520 seconds for the third time and so on.
Important Notes: 105 and 208 lcm
The below are the important notes to be remembered while solving the lcm of 105 and 208:
- The common prime factors and the remaining prime factors of 105 and 208 should be multiplied to find the least common multiple of 105 and 208, when solving lcm by using prime factors method.
- The results of lcm of 105 and 208, and the lcm of 208 and 105 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 105 and 208?
The below solved example with step by step work shows how to find what is the lcm of 105 and 208 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 105 and 208?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 105
B = 208
What to be found:
find the lcm of 105 and 208
step 2 Find the prime factors of 105 and 208:
Prime factors of 105 = 3 x 5 x 7
Prime factors of 208 = 2 x 2 x 2 x 2 x 13
step 3Identify the repeated and non-repeated prime factors of 105 and 208:
Since there is no common factors between 105 and 208, multiplying the given numbers directly provides the LCM of
105 and 208.
= 105 x 208
= 21840
lcm(105 and 208) = 21840
Hence,
lcm of 105 and 208 is 21840
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 105 and 208.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 105 and 208
What to be found:
lcm (105, 208) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
105 and 208
step 3 Choose the divisor which divides each or most of the given integers (105 and 208), 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 105 and 208 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 105 | 208 |
| 2 | 105 | 104 |
| 2 | 105 | 52 |
| 2 | 105 | 26 |
| 3 | 105 | 13 |
| 5 | 35 | 13 |
| 7 | 7 | 13 |
| 13 | 1 | 13 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 105 and 208:
= 2 x 2 x 2 x 2 x 3 x 5 x 7 x 13
= 21840
LCM(105, 208) = 21840
The LCM of two numbers 105 and 208 is 21840