LCM of 65 and 212
13780 is the LCM of 65 and 212. 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 212, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 65 and 212?
lcm (65 212) = (?)
65 => 5 x 13
212 => 2 x 2 x 53
= 5 x 13 x 2 x 2 x 53
= 13780
lcm (65 and 212) = 13780
13780 is the LCM of 65 and 212.
where,
65 is a positive integer,
212 is a positive integer,
13780 is the LCM of 65 and 212,
There is no common factors of 65 and 212 in {5 x 13, 2 x 2 x 53},
{5 x 13 x 2 x 2 x 53} in {5 x 13, 2 x 2 x 53} are the uncommon factors of 65 and 212.
Use in Mathematics: LCM of 65 and 212
The below are some of the mathematical applications where lcm of 65 and 212 can be used:
- to find the least number which is exactly divisible by 65 and 212.
- to find the common denominator for two fractions having 65 and 212 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 65 and 212 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 212 seconds repeatedly. The answer is that all bells A and B toll together at 13780 seconds for the first time, at 27560 seconds for the second time, at 41340 seconds for the third time and so on.
Important Notes: 65 and 212 lcm
The below are the important notes to be remembered while solving the lcm of 65 and 212:
- The common prime factors and the remaining prime factors of 65 and 212 should be multiplied to find the least common multiple of 65 and 212, when solving lcm by using prime factors method.
- The results of lcm of 65 and 212, and the lcm of 212 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 212?
The below solved example with step by step work shows how to find what is the lcm of 65 and 212 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 65 and 212?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 65
B = 212
What to be found:
find the lcm of 65 and 212
step 2 Find the prime factors of 65 and 212:
Prime factors of 65 = 5 x 13
Prime factors of 212 = 2 x 2 x 53
step 3Identify the repeated and non-repeated prime factors of 65 and 212:
Since there is no common factors between 65 and 212, multiplying the given numbers directly provides the LCM of
65 and 212.
= 65 x 212
= 13780
lcm(65 and 212) = 13780
Hence,
lcm of 65 and 212 is 13780
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 65 and 212.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 65 and 212
What to be found:
lcm (65, 212) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
65 and 212
step 3 Choose the divisor which divides each or most of the given integers (65 and 212), 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 212 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 65 | 212 |
| 2 | 65 | 106 |
| 5 | 65 | 53 |
| 13 | 13 | 53 |
| 53 | 1 | 53 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 65 and 212:
= 2 x 2 x 5 x 13 x 53
= 13780
LCM(65, 212) = 13780
The LCM of two numbers 65 and 212 is 13780