LCM of 18 and 133
2394 is the LCM of 18 and 133. 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 18 and 133, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 18 and 133?
lcm (18 133) = (?)
18 => 2 x 3 x 3
133 => 7 x 19
= 2 x 3 x 3 x 7 x 19
= 2394
lcm (18 and 133) = 2394
2394 is the LCM of 18 and 133.
where,
18 is a positive integer,
133 is a positive integer,
2394 is the LCM of 18 and 133,
There is no common factors of 18 and 133 in {2 x 3 x 3, 7 x 19},
{2 x 3 x 3 x 7 x 19} in {2 x 3 x 3, 7 x 19} are the uncommon factors of 18 and 133.
Use in Mathematics: LCM of 18 and 133
The below are some of the mathematical applications where lcm of 18 and 133 can be used:
- to find the least number which is exactly divisible by 18 and 133.
- to find the common denominator for two fractions having 18 and 133 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 18 and 133 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 18 seconds and bell B tolls at 133 seconds repeatedly. The answer is that all bells A and B toll together at 2394 seconds for the first time, at 4788 seconds for the second time, at 7182 seconds for the third time and so on.
Important Notes: 18 and 133 lcm
The below are the important notes to be remembered while solving the lcm of 18 and 133:
- The common prime factors and the remaining prime factors of 18 and 133 should be multiplied to find the least common multiple of 18 and 133, when solving lcm by using prime factors method.
- The results of lcm of 18 and 133, and the lcm of 133 and 18 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 18 and 133?
The below solved example with step by step work shows how to find what is the lcm of 18 and 133 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 18 and 133?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 18
B = 133
What to be found:
find the lcm of 18 and 133
step 2 Find the prime factors of 18 and 133:
Prime factors of 18 = 2 x 3 x 3
Prime factors of 133 = 7 x 19
step 3Identify the repeated and non-repeated prime factors of 18 and 133:
Since there is no common factors between 18 and 133, multiplying the given numbers directly provides the LCM of
18 and 133.
= 18 x 133
= 2394
lcm(18 and 133) = 2394
Hence,
lcm of 18 and 133 is 2394
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 18 and 133.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 18 and 133
What to be found:
lcm (18, 133) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
18 and 133
step 3 Choose the divisor which divides each or most of the given integers (18 and 133), 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 18 and 133 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 18 | 133 |
| 3 | 9 | 133 |
| 3 | 3 | 133 |
| 7 | 1 | 133 |
| 19 | 1 | 19 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 18 and 133:
= 2 x 3 x 3 x 7 x 19
= 2394
LCM(18, 133) = 2394
The LCM of two numbers 18 and 133 is 2394