LCM of 65 and 275
3575 is the LCM of 65 and 275. 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 65 and 275, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 65 and 275?
lcm (65 275) = (?)
65 => 5 x 13
275 => 5 x 5 x 11
= 5 x 13 x 5 x 11
= 3575
lcm (65 and 275) = 3575
3575 is the LCM of 65 and 275.
where,
65 is a positive integer,
275 is a positive integer,
3575 is the LCM of 65 and 275,
{5} in {5 x 13, 5 x 5 x 11} is the common factors of 65 and 275,
{13 x 5 x 11} in {5 x 13, 5 x 5 x 11} are the uncommon factors of 65 and 275.
Use in Mathematics: LCM of 65 and 275
The below are some of the mathematical applications where lcm of 65 and 275 can be used:
- to find the least number which is exactly divisible by 65 and 275.
- to find the common denominator for two fractions having 65 and 275 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 65 and 275 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 275 seconds repeatedly. The answer is that all bells A and B toll together at 3575 seconds for the first time, at 7150 seconds for the second time, at 10725 seconds for the third time and so on.
Important Notes: 65 and 275 lcm
The below are the important notes to be remembered while solving the lcm of 65 and 275:
- The common prime factors and the remaining prime factors of 65 and 275 should be multiplied to find the least common multiple of 65 and 275, when solving lcm by using prime factors method.
- The results of lcm of 65 and 275, and the lcm of 275 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 275?
The below solved example with step by step work shows how to find what is the lcm of 65 and 275 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 65 and 275?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 65
B = 275
What to be found:
find the lcm of 65 and 275
step 2 Find the prime factors of 65 and 275:
Prime factors of 65 = 5 x 13
Prime factors of 275 = 5 x 5 x 11
step 3 Identify the repeated and non-repeated prime factors of 65 and 275:
{5} is the most repeated factor and {13 x 5 x 11} are the non-repeated factors of 65 and 275.
step 4 Find the product of repeated and non-repeated prime factors of 65 and 275:
= 5 x 13 x 5 x 11
= 3575
lcm(65 and 275) = 3575
Hence,
lcm of 65 and 275 is 3575
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 65 and 275.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 65 and 275
What to be found:
lcm (65, 275) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
65 and 275
step 3 Choose the divisor which divides each or most of the given integers (65 and 275), 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 275 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 5 | 65 | 275 |
| 5 | 13 | 55 |
| 11 | 13 | 11 |
| 13 | 13 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 65 and 275:
= 5 x 5 x 11 x 13
= 3575
LCM(65, 275) = 3575
The LCM of two numbers 65 and 275 is 3575