LCM of 135 and 310
8370 is the LCM of 135 and 310. 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 135 and 310, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 135 and 310?
lcm (135 310) = (?)
135 => 3 x 3 x 3 x 5
310 => 2 x 5 x 31
= 5 x 3 x 3 x 3 x 2 x 31
= 8370
lcm (135 and 310) = 8370
8370 is the LCM of 135 and 310.
where,
135 is a positive integer,
310 is a positive integer,
8370 is the LCM of 135 and 310,
{5} in {3 x 3 x 3 x 5, 2 x 5 x 31} is the common factors of 135 and 310,
{3 x 3 x 3 x 2 x 31} in {3 x 3 x 3 x 5, 2 x 5 x 31} are the uncommon factors of 135 and 310.
Use in Mathematics: LCM of 135 and 310
The below are some of the mathematical applications where lcm of 135 and 310 can be used:
- to find the least number which is exactly divisible by 135 and 310.
- to find the common denominator for two fractions having 135 and 310 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 135 and 310 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 135 seconds and bell B tolls at 310 seconds repeatedly. The answer is that all bells A and B toll together at 8370 seconds for the first time, at 16740 seconds for the second time, at 25110 seconds for the third time and so on.
Important Notes: 135 and 310 lcm
The below are the important notes to be remembered while solving the lcm of 135 and 310:
- The common prime factors and the remaining prime factors of 135 and 310 should be multiplied to find the least common multiple of 135 and 310, when solving lcm by using prime factors method.
- The results of lcm of 135 and 310, and the lcm of 310 and 135 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 135 and 310?
The below solved example with step by step work shows how to find what is the lcm of 135 and 310 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 135 and 310?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 135
B = 310
What to be found:
find the lcm of 135 and 310
step 2 Find the prime factors of 135 and 310:
Prime factors of 135 = 3 x 3 x 3 x 5
Prime factors of 310 = 2 x 5 x 31
step 3 Identify the repeated and non-repeated prime factors of 135 and 310:
{5} is the most repeated factor and {3 x 3 x 3 x 2 x 31} are the non-repeated factors of 135 and 310.
step 4 Find the product of repeated and non-repeated prime factors of 135 and 310:
= 5 x 3 x 3 x 3 x 2 x 31
= 8370
lcm(135 and 310) = 8370
Hence,
lcm of 135 and 310 is 8370
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 135 and 310.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 135 and 310
What to be found:
lcm (135, 310) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
135 and 310
step 3 Choose the divisor which divides each or most of the given integers (135 and 310), 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 135 and 310 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 135 | 310 |
| 3 | 135 | 155 |
| 3 | 45 | 155 |
| 3 | 15 | 155 |
| 5 | 5 | 155 |
| 31 | 1 | 31 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 135 and 310:
= 2 x 3 x 3 x 3 x 5 x 31
= 8370
LCM(135, 310) = 8370
The LCM of two numbers 135 and 310 is 8370