105 and 195 LCM
LCM of 105 and 195 is equal to 1365. The comprehensive work provides more insight of how to find what is the lcm of 105 and 195 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 105 and 195?
lcm (105 195) = (?)
105 => 3 x 5 x 7
195 => 3 x 5 x 13
= 3 x 5 x 7 x 13
= 1365
lcm (105 and 195) = 1365
1365 is the lcm of 105 and 195.
where,
105 is a positive integer,
195 is a positive integer,
1365 is the lcm of 105 and 195,
{3 x 5} in {3 x 5 x 7, 3 x 5 x 13} are the common factors of 105 and 195,
{7 x 13} in {3 x 5 x 7, 3 x 5 x 13} are the uncommon factors of 105 and 195.
Use in Mathematics: LCM of 105 and 195
The below are some of the mathematical applications where lcm of 105 and 195 can be used:
- to find the least number which is exactly divisible by 105 and 195.
- to find the common denominator for two fractions having 105 and 195 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 105 and 195 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 195 seconds repeatedly. The answer is that all bells A and B toll together at 1365 seconds for the first time, at 2730 seconds for the second time, at 4095 seconds for the third time and so on.
Important Notes: 105 and 195 lcm
The below are the important notes to be remembered while solving the lcm of 105 and 195:
- The common prime factors and the remaining prime factors of 105 and 195 should be multiplied to find the least common multiple of 105 and 195, when solving lcm by using prime factors method.
- The results of lcm of 105 and 195, and the lcm of 195 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 195?
The below solved example with step by step work shows how to find what is the lcm of 105 and 195 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 105 and 195?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 105
B = 195
What to be found:
find the lcm of 105 and 195
step 2 Find the prime factors of 105 and 195:
Prime factors of 105 = 3 x 5 x 7
Prime factors of 195 = 3 x 5 x 13
step 3 Identify the repeated and non-repeated prime factors of 105 and 195:
{3, 5} are the most repeated factors and {7 x 13} are the non-repeated factors of 105 and 195.
step 4 Find the product of repeated and non-repeated prime factors of 105 and 195:
= 3 x 5 x 7 x 13
= 1365
lcm(105 and 195) = 1365
Hence,
lcm of 105 and 195 is 1365
This special division method is the easiest way to understand the entire calculation of what is the lcm of 105 and 195.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 105 and 195
What to be found:
lcm (105, 195) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
105 and 195
step 3 Choose the divisor which divides each or most of the given integers (105 and 195), 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 195 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 105 | 195 |
| 5 | 35 | 65 |
| 7 | 7 | 13 |
| 13 | 1 | 13 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 105 and 195:
= 3 x 5 x 7 x 13
= 1365
LCM(105, 195) = 1365
The least common multiple for two numbers 105 and 195 is 1365