LCM of 189 and 242
45738 is the LCM of 189 and 242. 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 189 and 242, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 189 and 242?
lcm (189 242) = (?)
189 => 3 x 3 x 3 x 7
242 => 2 x 11 x 11
= 3 x 3 x 3 x 7 x 2 x 11 x 11
= 45738
lcm (189 and 242) = 45738
45738 is the LCM of 189 and 242.
where,
189 is a positive integer,
242 is a positive integer,
45738 is the LCM of 189 and 242,
There is no common factors of 189 and 242 in {3 x 3 x 3 x 7, 2 x 11 x 11},
{3 x 3 x 3 x 7 x 2 x 11 x 11} in {3 x 3 x 3 x 7, 2 x 11 x 11} are the uncommon factors of 189 and 242.
Use in Mathematics: LCM of 189 and 242
The below are some of the mathematical applications where lcm of 189 and 242 can be used:
- to find the least number which is exactly divisible by 189 and 242.
- to find the common denominator for two fractions having 189 and 242 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 189 and 242 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 189 seconds and bell B tolls at 242 seconds repeatedly. The answer is that all bells A and B toll together at 45738 seconds for the first time, at 91476 seconds for the second time, at 137214 seconds for the third time and so on.
Important Notes: 189 and 242 lcm
The below are the important notes to be remembered while solving the lcm of 189 and 242:
- The common prime factors and the remaining prime factors of 189 and 242 should be multiplied to find the least common multiple of 189 and 242, when solving lcm by using prime factors method.
- The results of lcm of 189 and 242, and the lcm of 242 and 189 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 189 and 242?
The below solved example with step by step work shows how to find what is the lcm of 189 and 242 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 189 and 242?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 189
B = 242
What to be found:
find the lcm of 189 and 242
step 2 Find the prime factors of 189 and 242:
Prime factors of 189 = 3 x 3 x 3 x 7
Prime factors of 242 = 2 x 11 x 11
step 3Identify the repeated and non-repeated prime factors of 189 and 242:
Since there is no common factors between 189 and 242, multiplying the given numbers directly provides the LCM of
189 and 242.
= 189 x 242
= 45738
lcm(189 and 242) = 45738
Hence,
lcm of 189 and 242 is 45738
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 189 and 242.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 189 and 242
What to be found:
lcm (189, 242) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
189 and 242
step 3 Choose the divisor which divides each or most of the given integers (189 and 242), 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 189 and 242 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 189 | 242 |
| 3 | 189 | 121 |
| 3 | 63 | 121 |
| 3 | 21 | 121 |
| 7 | 7 | 121 |
| 11 | 1 | 121 |
| 11 | 1 | 11 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 189 and 242:
= 2 x 3 x 3 x 3 x 7 x 11 x 11
= 45738
LCM(189, 242) = 45738
The LCM of two numbers 189 and 242 is 45738