LCM of 105 and 135
945 is the LCM of 105 and 135. 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 135, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 105 and 135?
lcm (105 135) = (?)
105 => 3 x 5 x 7
135 => 3 x 3 x 3 x 5
= 3 x 5 x 7 x 3 x 3
= 945
lcm (105 and 135) = 945
945 is the LCM of 105 and 135.
where,
105 is a positive integer,
135 is a positive integer,
945 is the LCM of 105 and 135,
{3 x 5} in {3 x 5 x 7, 3 x 3 x 3 x 5} are the common factors of 105 and 135,
{7 x 3 x 3} in {3 x 5 x 7, 3 x 3 x 3 x 5} are the uncommon factors of 105 and 135.
Use in Mathematics: LCM of 105 and 135
The below are some of the mathematical applications where lcm of 105 and 135 can be used:
- to find the least number which is exactly divisible by 105 and 135.
- to find the common denominator for two fractions having 105 and 135 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 105 and 135 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 135 seconds repeatedly. The answer is that all bells A and B toll together at 945 seconds for the first time, at 1890 seconds for the second time, at 2835 seconds for the third time and so on.
Important Notes: 105 and 135 lcm
The below are the important notes to be remembered while solving the lcm of 105 and 135:
- The common prime factors and the remaining prime factors of 105 and 135 should be multiplied to find the least common multiple of 105 and 135, when solving lcm by using prime factors method.
- The results of lcm of 105 and 135, and the lcm of 135 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 135?
The below solved example with step by step work shows how to find what is the lcm of 105 and 135 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 105 and 135?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 105
B = 135
What to be found:
find the lcm of 105 and 135
step 2 Find the prime factors of 105 and 135:
Prime factors of 105 = 3 x 5 x 7
Prime factors of 135 = 3 x 3 x 3 x 5
step 3 Identify the repeated and non-repeated prime factors of 105 and 135:
{3, 5} are the most repeated factors and {7 x 3 x 3} are the non-repeated factors of 105 and 135.
step 4 Find the product of repeated and non-repeated prime factors of 105 and 135:
= 3 x 5 x 7 x 3 x 3
= 945
lcm(105 and 135) = 945
Hence,
lcm of 105 and 135 is 945
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 105 and 135.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 105 and 135
What to be found:
lcm (105, 135) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
105 and 135
step 3 Choose the divisor which divides each or most of the given integers (105 and 135), 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 135 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 105 | 135 |
| 3 | 35 | 45 |
| 3 | 35 | 15 |
| 5 | 35 | 5 |
| 7 | 7 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 105 and 135:
= 3 x 3 x 3 x 5 x 7
= 945
LCM(105, 135) = 945
The LCM of two numbers 105 and 135 is 945