LCM of 138 and 266
18354 is the LCM of 138 and 266. 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 138 and 266, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 138 and 266?
lcm (138 266) = (?)
138 => 2 x 3 x 23
266 => 2 x 7 x 19
= 2 x 3 x 23 x 7 x 19
= 18354
lcm (138 and 266) = 18354
18354 is the LCM of 138 and 266.
where,
138 is a positive integer,
266 is a positive integer,
18354 is the LCM of 138 and 266,
{2} in {2 x 3 x 23, 2 x 7 x 19} is the common factors of 138 and 266,
{3 x 23 x 7 x 19} in {2 x 3 x 23, 2 x 7 x 19} are the uncommon factors of 138 and 266.
Use in Mathematics: LCM of 138 and 266
The below are some of the mathematical applications where lcm of 138 and 266 can be used:
- to find the least number which is exactly divisible by 138 and 266.
- to find the common denominator for two fractions having 138 and 266 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 138 and 266 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 138 seconds and bell B tolls at 266 seconds repeatedly. The answer is that all bells A and B toll together at 18354 seconds for the first time, at 36708 seconds for the second time, at 55062 seconds for the third time and so on.
Important Notes: 138 and 266 lcm
The below are the important notes to be remembered while solving the lcm of 138 and 266:
- The common prime factors and the remaining prime factors of 138 and 266 should be multiplied to find the least common multiple of 138 and 266, when solving lcm by using prime factors method.
- The results of lcm of 138 and 266, and the lcm of 266 and 138 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 138 and 266?
The below solved example with step by step work shows how to find what is the lcm of 138 and 266 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 138 and 266?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 138
B = 266
What to be found:
find the lcm of 138 and 266
step 2 Find the prime factors of 138 and 266:
Prime factors of 138 = 2 x 3 x 23
Prime factors of 266 = 2 x 7 x 19
step 3 Identify the repeated and non-repeated prime factors of 138 and 266:
{2} is the most repeated factor and {3 x 23 x 7 x 19} are the non-repeated factors of 138 and 266.
step 4 Find the product of repeated and non-repeated prime factors of 138 and 266:
= 2 x 3 x 23 x 7 x 19
= 18354
lcm(138 and 266) = 18354
Hence,
lcm of 138 and 266 is 18354
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 138 and 266.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 138 and 266
What to be found:
lcm (138, 266) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
138 and 266
step 3 Choose the divisor which divides each or most of the given integers (138 and 266), 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 138 and 266 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 138 | 266 |
| 3 | 69 | 133 |
| 7 | 23 | 133 |
| 19 | 23 | 19 |
| 23 | 23 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 138 and 266:
= 2 x 3 x 7 x 19 x 23
= 18354
LCM(138, 266) = 18354
The LCM of two numbers 138 and 266 is 18354