65 and 130 LCM
LCM of 65 and 130 is equal to 130. The comprehensive work provides more insight of how to find what is the lcm of 65 and 130 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 65 and 130?
lcm (65 130) = (?)
65 => 5 x 13
130 => 2 x 5 x 13
= 5 x 13 x 2
= 130
lcm (65 and 130) = 130
130 is the lcm of 65 and 130.
where,
65 is a positive integer,
130 is a positive integer,
130 is the lcm of 65 and 130,
{5 x 13} in {5 x 13, 2 x 5 x 13} are the common factors of 65 and 130,
{2} in {5 x 13, 2 x 5 x 13} is the uncommon factors of 65 and 130.
Use in Mathematics: LCM of 65 and 130
The below are some of the mathematical applications where lcm of 65 and 130 can be used:
- to find the least number which is exactly divisible by 65 and 130.
- to find the common denominator for two fractions having 65 and 130 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 65 and 130 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 65 seconds and bell B tolls at 130 seconds repeatedly. The answer is that all bells A and B toll together at 130 seconds for the first time, at 260 seconds for the second time, at 390 seconds for the third time and so on.
Important Notes: 65 and 130 lcm
The below are the important notes to be remembered while solving the lcm of 65 and 130:
- The common prime factors and the remaining prime factors of 65 and 130 should be multiplied to find the least common multiple of 65 and 130, when solving lcm by using prime factors method.
- The results of lcm of 65 and 130, and the lcm of 130 and 65 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 65 and 130?
The below solved example with step by step work shows how to find what is the lcm of 65 and 130 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 65 and 130?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 65
B = 130
What to be found:
find the lcm of 65 and 130
step 2 Find the prime factors of 65 and 130:
Prime factors of 65 = 5 x 13
Prime factors of 130 = 2 x 5 x 13
step 3 Identify the repeated and non-repeated prime factors of 65 and 130:
{5, 13} are the most repeated factors and {2} is the non-repeated factor of 65 and 130.
step 4 Find the product of repeated and non-repeated prime factors of 65 and 130:
= 5 x 13 x 2
= 130
lcm(65 and 130) = 130
Hence,
lcm of 65 and 130 is 130
This special division method is the easiest way to understand the entire calculation of what is the lcm of 65 and 130.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 65 and 130
What to be found:
lcm (65, 130) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
65 and 130
step 3 Choose the divisor which divides each or most of the given integers (65 and 130), 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 65 and 130 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 65 | 130 |
| 5 | 65 | 65 |
| 13 | 13 | 13 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 65 and 130:
= 2 x 5 x 13
= 130
LCM(65, 130) = 130
The least common multiple for two numbers 65 and 130 is 130