LCM of 222 and 285
21090 is the LCM of 222 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 222 and 285, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 222 and 285?
lcm (222 285) = (?)
222 => 2 x 3 x 37
285 => 3 x 5 x 19
= 3 x 2 x 37 x 5 x 19
= 21090
lcm (222 and 285) = 21090
21090 is the LCM of 222 and 285.
where,
222 is a positive integer,
285 is a positive integer,
21090 is the LCM of 222 and 285,
{3} in {2 x 3 x 37, 3 x 5 x 19} is the common factors of 222 and 285,
{2 x 37 x 5 x 19} in {2 x 3 x 37, 3 x 5 x 19} are the uncommon factors of 222 and 285.
Use in Mathematics: LCM of 222 and 285
The below are some of the mathematical applications where lcm of 222 and 285 can be used:
- to find the least number which is exactly divisible by 222 and 285.
- to find the common denominator for two fractions having 222 and 285 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 222 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 222 seconds and bell B tolls at 285 seconds repeatedly. The answer is that all bells A and B toll together at 21090 seconds for the first time, at 42180 seconds for the second time, at 63270 seconds for the third time and so on.
Important Notes: 222 and 285 lcm
The below are the important notes to be remembered while solving the lcm of 222 and 285:
- The common prime factors and the remaining prime factors of 222 and 285 should be multiplied to find the least common multiple of 222 and 285, when solving lcm by using prime factors method.
- The results of lcm of 222 and 285, and the lcm of 285 and 222 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 222 and 285?
The below solved example with step by step work shows how to find what is the lcm of 222 and 285 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 222 and 285?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 222
B = 285
What to be found:
find the lcm of 222 and 285
step 2 Find the prime factors of 222 and 285:
Prime factors of 222 = 2 x 3 x 37
Prime factors of 285 = 3 x 5 x 19
step 3 Identify the repeated and non-repeated prime factors of 222 and 285:
{3} is the most repeated factor and {2 x 37 x 5 x 19} are the non-repeated factors of 222 and 285.
step 4 Find the product of repeated and non-repeated prime factors of 222 and 285:
= 3 x 2 x 37 x 5 x 19
= 21090
lcm(222 and 285) = 21090
Hence,
lcm of 222 and 285 is 21090
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 222 and 285.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 222 and 285
What to be found:
lcm (222, 285) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
222 and 285
step 3 Choose the divisor which divides each or most of the given integers (222 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 222 and 285 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 222 | 285 |
| 3 | 111 | 285 |
| 5 | 37 | 95 |
| 19 | 37 | 19 |
| 37 | 37 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 222 and 285:
= 2 x 3 x 5 x 19 x 37
= 21090
LCM(222, 285) = 21090
The LCM of two numbers 222 and 285 is 21090