LCM of 285 and 349
99465 is the LCM of 285 and 349. 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 285 and 349, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 285 and 349?
lcm (285 349) = (?)
285 => 3 x 5 x 19
349 => 349
= 3 x 5 x 19 x 349
= 99465
lcm (285 and 349) = 99465
99465 is the LCM of 285 and 349.
where,
285 is a positive integer,
349 is a positive integer,
99465 is the LCM of 285 and 349,
There is no common factors of 285 and 349 in {3 x 5 x 19, 349},
{3 x 5 x 19 x 349} in {3 x 5 x 19, 349} are the uncommon factors of 285 and 349.
Use in Mathematics: LCM of 285 and 349
The below are some of the mathematical applications where lcm of 285 and 349 can be used:
- to find the least number which is exactly divisible by 285 and 349.
- to find the common denominator for two fractions having 285 and 349 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 285 and 349 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 285 seconds and bell B tolls at 349 seconds repeatedly. The answer is that all bells A and B toll together at 99465 seconds for the first time, at 198930 seconds for the second time, at 298395 seconds for the third time and so on.
Important Notes: 285 and 349 lcm
The below are the important notes to be remembered while solving the lcm of 285 and 349:
- The common prime factors and the remaining prime factors of 285 and 349 should be multiplied to find the least common multiple of 285 and 349, when solving lcm by using prime factors method.
- The results of lcm of 285 and 349, and the lcm of 349 and 285 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 285 and 349?
The below solved example with step by step work shows how to find what is the lcm of 285 and 349 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 285 and 349?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 285
B = 349
What to be found:
find the lcm of 285 and 349
step 2 Find the prime factors of 285 and 349:
Prime factors of 285 = 3 x 5 x 19
Prime factors of 349 = 349
step 3Identify the repeated and non-repeated prime factors of 285 and 349:
Since there is no common factors between 285 and 349, multiplying the given numbers directly provides the LCM of
285 and 349.
= 285 x 349
= 99465
lcm(285 and 349) = 99465
Hence,
lcm of 285 and 349 is 99465
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 285 and 349.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 285 and 349
What to be found:
lcm (285, 349) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
285 and 349
step 3 Choose the divisor which divides each or most of the given integers (285 and 349), 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 285 and 349 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 285 | 349 |
| 5 | 95 | 349 |
| 19 | 19 | 349 |
| 349 | 1 | 349 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 285 and 349:
= 3 x 5 x 19 x 349
= 99465
LCM(285, 349) = 99465
The LCM of two numbers 285 and 349 is 99465