52 and 138 LCM
LCM of 52 and 138 is equal to 3588. The comprehensive work provides more insight of how to find what is the lcm of 52 and 138 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 52 and 138?
lcm (52 138) = (?)
52 => 2 x 2 x 13
138 => 2 x 3 x 23
= 2 x 2 x 13 x 3 x 23
= 3588
lcm (52 and 138) = 3588
3588 is the lcm of 52 and 138.
where,
52 is a positive integer,
138 is a positive integer,
3588 is the lcm of 52 and 138,
{2} in {2 x 2 x 13, 2 x 3 x 23} is the common factors of 52 and 138,
{2 x 13 x 3 x 23} in {2 x 2 x 13, 2 x 3 x 23} are the uncommon factors of 52 and 138.
Use in Mathematics: LCM of 52 and 138
The below are some of the mathematical applications where lcm of 52 and 138 can be used:
- to find the least number which is exactly divisible by 52 and 138.
- to find the common denominator for two fractions having 52 and 138 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 52 and 138 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 52 seconds and bell B tolls at 138 seconds repeatedly. The answer is that all bells A and B toll together at 3588 seconds for the first time, at 7176 seconds for the second time, at 10764 seconds for the third time and so on.
Important Notes: 52 and 138 lcm
The below are the important notes to be remembered while solving the lcm of 52 and 138:
- The common prime factors and the remaining prime factors of 52 and 138 should be multiplied to find the least common multiple of 52 and 138, when solving lcm by using prime factors method.
- The results of lcm of 52 and 138, and the lcm of 138 and 52 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 52 and 138?
The below solved example with step by step work shows how to find what is the lcm of 52 and 138 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 52 and 138?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 52
B = 138
What to be found:
find the lcm of 52 and 138
step 2 Find the prime factors of 52 and 138:
Prime factors of 52 = 2 x 2 x 13
Prime factors of 138 = 2 x 3 x 23
step 3 Identify the repeated and non-repeated prime factors of 52 and 138:
{2} is the most repeated factor and {2 x 13 x 3 x 23} are the non-repeated factors of 52 and 138.
step 4 Find the product of repeated and non-repeated prime factors of 52 and 138:
= 2 x 2 x 13 x 3 x 23
= 3588
lcm(52 and 138) = 3588
Hence,
lcm of 52 and 138 is 3588
This special division method is the easiest way to understand the entire calculation of what is the lcm of 52 and 138.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 52 and 138
What to be found:
lcm (52, 138) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
52 and 138
step 3 Choose the divisor which divides each or most of the given integers (52 and 138), 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 52 and 138 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 52 | 138 |
| 2 | 26 | 69 |
| 3 | 13 | 69 |
| 13 | 13 | 23 |
| 23 | 1 | 23 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 52 and 138:
= 2 x 2 x 3 x 13 x 23
= 3588
LCM(52, 138) = 3588
The least common multiple for two numbers 52 and 138 is 3588