LCM of 107 and 285
30495 is the LCM of 107 and 285. 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 107 and 285, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 107 and 285?
lcm (107 285) = (?)
107 => 107
285 => 3 x 5 x 19
= 107 x 3 x 5 x 19
= 30495
lcm (107 and 285) = 30495
30495 is the LCM of 107 and 285.
where,
107 is a positive integer,
285 is a positive integer,
30495 is the LCM of 107 and 285,
There is no common factors of 107 and 285 in {107, 3 x 5 x 19},
{107 x 3 x 5 x 19} in {107, 3 x 5 x 19} are the uncommon factors of 107 and 285.
Use in Mathematics: LCM of 107 and 285
The below are some of the mathematical applications where lcm of 107 and 285 can be used:
- to find the least number which is exactly divisible by 107 and 285.
- to find the common denominator for two fractions having 107 and 285 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 107 and 285 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 107 seconds and bell B tolls at 285 seconds repeatedly. The answer is that all bells A and B toll together at 30495 seconds for the first time, at 60990 seconds for the second time, at 91485 seconds for the third time and so on.
Important Notes: 107 and 285 lcm
The below are the important notes to be remembered while solving the lcm of 107 and 285:
- The common prime factors and the remaining prime factors of 107 and 285 should be multiplied to find the least common multiple of 107 and 285, when solving lcm by using prime factors method.
- The results of lcm of 107 and 285, and the lcm of 285 and 107 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 107 and 285?
The below solved example with step by step work shows how to find what is the lcm of 107 and 285 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 107 and 285?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 107
B = 285
What to be found:
find the lcm of 107 and 285
step 2 Find the prime factors of 107 and 285:
Prime factors of 107 = 107
Prime factors of 285 = 3 x 5 x 19
step 3Identify the repeated and non-repeated prime factors of 107 and 285:
Since there is no common factors between 107 and 285, multiplying the given numbers directly provides the LCM of
107 and 285.
= 107 x 285
= 30495
lcm(107 and 285) = 30495
Hence,
lcm of 107 and 285 is 30495
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 107 and 285.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 107 and 285
What to be found:
lcm (107, 285) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
107 and 285
step 3 Choose the divisor which divides each or most of the given integers (107 and 285), 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 107 and 285 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 107 | 285 |
| 5 | 107 | 95 |
| 19 | 107 | 19 |
| 107 | 107 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 107 and 285:
= 3 x 5 x 19 x 107
= 30495
LCM(107, 285) = 30495
The LCM of two numbers 107 and 285 is 30495