LCM of 234 and 313
73242 is the LCM of 234 and 313. 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 234 and 313, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 234 and 313?
lcm (234 313) = (?)
234 => 2 x 3 x 3 x 13
313 => 313
= 2 x 3 x 3 x 13 x 313
= 73242
lcm (234 and 313) = 73242
73242 is the LCM of 234 and 313.
where,
234 is a positive integer,
313 is a positive integer,
73242 is the LCM of 234 and 313,
There is no common factors of 234 and 313 in {2 x 3 x 3 x 13, 313},
{2 x 3 x 3 x 13 x 313} in {2 x 3 x 3 x 13, 313} are the uncommon factors of 234 and 313.
Use in Mathematics: LCM of 234 and 313
The below are some of the mathematical applications where lcm of 234 and 313 can be used:
- to find the least number which is exactly divisible by 234 and 313.
- to find the common denominator for two fractions having 234 and 313 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 234 and 313 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 234 seconds and bell B tolls at 313 seconds repeatedly. The answer is that all bells A and B toll together at 73242 seconds for the first time, at 146484 seconds for the second time, at 219726 seconds for the third time and so on.
Important Notes: 234 and 313 lcm
The below are the important notes to be remembered while solving the lcm of 234 and 313:
- The common prime factors and the remaining prime factors of 234 and 313 should be multiplied to find the least common multiple of 234 and 313, when solving lcm by using prime factors method.
- The results of lcm of 234 and 313, and the lcm of 313 and 234 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 234 and 313?
The below solved example with step by step work shows how to find what is the lcm of 234 and 313 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 234 and 313?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 234
B = 313
What to be found:
find the lcm of 234 and 313
step 2 Find the prime factors of 234 and 313:
Prime factors of 234 = 2 x 3 x 3 x 13
Prime factors of 313 = 313
step 3Identify the repeated and non-repeated prime factors of 234 and 313:
Since there is no common factors between 234 and 313, multiplying the given numbers directly provides the LCM of
234 and 313.
= 234 x 313
= 73242
lcm(234 and 313) = 73242
Hence,
lcm of 234 and 313 is 73242
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 234 and 313.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 234 and 313
What to be found:
lcm (234, 313) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
234 and 313
step 3 Choose the divisor which divides each or most of the given integers (234 and 313), 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 234 and 313 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 234 | 313 |
| 3 | 117 | 313 |
| 3 | 39 | 313 |
| 13 | 13 | 313 |
| 313 | 1 | 313 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 234 and 313:
= 2 x 3 x 3 x 13 x 313
= 73242
LCM(234, 313) = 73242
The LCM of two numbers 234 and 313 is 73242