LCM of 138 and 160
11040 is the LCM of 138 and 160. 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 160, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 138 and 160?
lcm (138 160) = (?)
138 => 2 x 3 x 23
160 => 2 x 2 x 2 x 2 x 2 x 5
= 2 x 3 x 23 x 2 x 2 x 2 x 2 x 5
= 11040
lcm (138 and 160) = 11040
11040 is the LCM of 138 and 160.
where,
138 is a positive integer,
160 is a positive integer,
11040 is the LCM of 138 and 160,
{2} in {2 x 3 x 23, 2 x 2 x 2 x 2 x 2 x 5} is the common factors of 138 and 160,
{3 x 23 x 2 x 2 x 2 x 2 x 5} in {2 x 3 x 23, 2 x 2 x 2 x 2 x 2 x 5} are the uncommon factors of 138 and 160.
Use in Mathematics: LCM of 138 and 160
The below are some of the mathematical applications where lcm of 138 and 160 can be used:
- to find the least number which is exactly divisible by 138 and 160.
- to find the common denominator for two fractions having 138 and 160 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 138 and 160 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 160 seconds repeatedly. The answer is that all bells A and B toll together at 11040 seconds for the first time, at 22080 seconds for the second time, at 33120 seconds for the third time and so on.
Important Notes: 138 and 160 lcm
The below are the important notes to be remembered while solving the lcm of 138 and 160:
- The common prime factors and the remaining prime factors of 138 and 160 should be multiplied to find the least common multiple of 138 and 160, when solving lcm by using prime factors method.
- The results of lcm of 138 and 160, and the lcm of 160 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 160?
The below solved example with step by step work shows how to find what is the lcm of 138 and 160 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 138 and 160?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 138
B = 160
What to be found:
find the lcm of 138 and 160
step 2 Find the prime factors of 138 and 160:
Prime factors of 138 = 2 x 3 x 23
Prime factors of 160 = 2 x 2 x 2 x 2 x 2 x 5
step 3 Identify the repeated and non-repeated prime factors of 138 and 160:
{2} is the most repeated factor and {3 x 23 x 2 x 2 x 2 x 2 x 5} are the non-repeated factors of 138 and 160.
step 4 Find the product of repeated and non-repeated prime factors of 138 and 160:
= 2 x 3 x 23 x 2 x 2 x 2 x 2 x 5
= 11040
lcm(138 and 160) = 11040
Hence,
lcm of 138 and 160 is 11040
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 138 and 160.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 138 and 160
What to be found:
lcm (138, 160) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
138 and 160
step 3 Choose the divisor which divides each or most of the given integers (138 and 160), 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 160 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 138 | 160 |
| 2 | 69 | 80 |
| 2 | 69 | 40 |
| 2 | 69 | 20 |
| 2 | 69 | 10 |
| 3 | 69 | 5 |
| 5 | 23 | 5 |
| 23 | 23 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 138 and 160:
= 2 x 2 x 2 x 2 x 2 x 3 x 5 x 23
= 11040
LCM(138, 160) = 11040
The LCM of two numbers 138 and 160 is 11040