LCM of 105 and 122
12810 is the LCM of 105 and 122. 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 122, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 105 and 122?
lcm (105 122) = (?)
105 => 3 x 5 x 7
122 => 2 x 61
= 3 x 5 x 7 x 2 x 61
= 12810
lcm (105 and 122) = 12810
12810 is the LCM of 105 and 122.
where,
105 is a positive integer,
122 is a positive integer,
12810 is the LCM of 105 and 122,
There is no common factors of 105 and 122 in {3 x 5 x 7, 2 x 61},
{3 x 5 x 7 x 2 x 61} in {3 x 5 x 7, 2 x 61} are the uncommon factors of 105 and 122.
Use in Mathematics: LCM of 105 and 122
The below are some of the mathematical applications where lcm of 105 and 122 can be used:
- to find the least number which is exactly divisible by 105 and 122.
- to find the common denominator for two fractions having 105 and 122 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 105 and 122 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 122 seconds repeatedly. The answer is that all bells A and B toll together at 12810 seconds for the first time, at 25620 seconds for the second time, at 38430 seconds for the third time and so on.
Important Notes: 105 and 122 lcm
The below are the important notes to be remembered while solving the lcm of 105 and 122:
- The common prime factors and the remaining prime factors of 105 and 122 should be multiplied to find the least common multiple of 105 and 122, when solving lcm by using prime factors method.
- The results of lcm of 105 and 122, and the lcm of 122 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 122?
The below solved example with step by step work shows how to find what is the lcm of 105 and 122 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 105 and 122?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 105
B = 122
What to be found:
find the lcm of 105 and 122
step 2 Find the prime factors of 105 and 122:
Prime factors of 105 = 3 x 5 x 7
Prime factors of 122 = 2 x 61
step 3Identify the repeated and non-repeated prime factors of 105 and 122:
Since there is no common factors between 105 and 122, multiplying the given numbers directly provides the LCM of
105 and 122.
= 105 x 122
= 12810
lcm(105 and 122) = 12810
Hence,
lcm of 105 and 122 is 12810
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 105 and 122.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 105 and 122
What to be found:
lcm (105, 122) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
105 and 122
step 3 Choose the divisor which divides each or most of the given integers (105 and 122), 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 122 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 105 | 122 |
| 3 | 105 | 61 |
| 5 | 35 | 61 |
| 7 | 7 | 61 |
| 61 | 1 | 61 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 105 and 122:
= 2 x 3 x 5 x 7 x 61
= 12810
LCM(105, 122) = 12810
The LCM of two numbers 105 and 122 is 12810