LCM of 189 and 272
51408 is the LCM of 189 and 272. 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 272, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 189 and 272?
lcm (189 272) = (?)
189 => 3 x 3 x 3 x 7
272 => 2 x 2 x 2 x 2 x 17
= 3 x 3 x 3 x 7 x 2 x 2 x 2 x 2 x 17
= 51408
lcm (189 and 272) = 51408
51408 is the LCM of 189 and 272.
where,
189 is a positive integer,
272 is a positive integer,
51408 is the LCM of 189 and 272,
There is no common factors of 189 and 272 in {3 x 3 x 3 x 7, 2 x 2 x 2 x 2 x 17},
{3 x 3 x 3 x 7 x 2 x 2 x 2 x 2 x 17} in {3 x 3 x 3 x 7, 2 x 2 x 2 x 2 x 17} are the uncommon factors of 189 and 272.
Use in Mathematics: LCM of 189 and 272
The below are some of the mathematical applications where lcm of 189 and 272 can be used:
- to find the least number which is exactly divisible by 189 and 272.
- to find the common denominator for two fractions having 189 and 272 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 189 and 272 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 272 seconds repeatedly. The answer is that all bells A and B toll together at 51408 seconds for the first time, at 102816 seconds for the second time, at 154224 seconds for the third time and so on.
Important Notes: 189 and 272 lcm
The below are the important notes to be remembered while solving the lcm of 189 and 272:
- The common prime factors and the remaining prime factors of 189 and 272 should be multiplied to find the least common multiple of 189 and 272, when solving lcm by using prime factors method.
- The results of lcm of 189 and 272, and the lcm of 272 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 272?
The below solved example with step by step work shows how to find what is the lcm of 189 and 272 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 189 and 272?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 189
B = 272
What to be found:
find the lcm of 189 and 272
step 2 Find the prime factors of 189 and 272:
Prime factors of 189 = 3 x 3 x 3 x 7
Prime factors of 272 = 2 x 2 x 2 x 2 x 17
step 3Identify the repeated and non-repeated prime factors of 189 and 272:
Since there is no common factors between 189 and 272, multiplying the given numbers directly provides the LCM of
189 and 272.
= 189 x 272
= 51408
lcm(189 and 272) = 51408
Hence,
lcm of 189 and 272 is 51408
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 189 and 272.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 189 and 272
What to be found:
lcm (189, 272) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
189 and 272
step 3 Choose the divisor which divides each or most of the given integers (189 and 272), 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 272 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 189 | 272 |
| 2 | 189 | 136 |
| 2 | 189 | 68 |
| 2 | 189 | 34 |
| 3 | 189 | 17 |
| 3 | 63 | 17 |
| 3 | 21 | 17 |
| 7 | 7 | 17 |
| 17 | 1 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 189 and 272:
= 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 x 17
= 51408
LCM(189, 272) = 51408
The LCM of two numbers 189 and 272 is 51408