LCM of 39 and 118
4602 is the LCM of 39 and 118. 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 39 and 118, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 39 and 118?
lcm (39 118) = (?)
39 => 3 x 13
118 => 2 x 59
= 3 x 13 x 2 x 59
= 4602
lcm (39 and 118) = 4602
4602 is the LCM of 39 and 118.
where,
39 is a positive integer,
118 is a positive integer,
4602 is the LCM of 39 and 118,
There is no common factors of 39 and 118 in {3 x 13, 2 x 59},
{3 x 13 x 2 x 59} in {3 x 13, 2 x 59} are the uncommon factors of 39 and 118.
Use in Mathematics: LCM of 39 and 118
The below are some of the mathematical applications where lcm of 39 and 118 can be used:
- to find the least number which is exactly divisible by 39 and 118.
- to find the common denominator for two fractions having 39 and 118 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 39 and 118 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 39 seconds and bell B tolls at 118 seconds repeatedly. The answer is that all bells A and B toll together at 4602 seconds for the first time, at 9204 seconds for the second time, at 13806 seconds for the third time and so on.
Important Notes: 39 and 118 lcm
The below are the important notes to be remembered while solving the lcm of 39 and 118:
- The common prime factors and the remaining prime factors of 39 and 118 should be multiplied to find the least common multiple of 39 and 118, when solving lcm by using prime factors method.
- The results of lcm of 39 and 118, and the lcm of 118 and 39 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 39 and 118?
The below solved example with step by step work shows how to find what is the lcm of 39 and 118 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 39 and 118?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 39
B = 118
What to be found:
find the lcm of 39 and 118
step 2 Find the prime factors of 39 and 118:
Prime factors of 39 = 3 x 13
Prime factors of 118 = 2 x 59
step 3Identify the repeated and non-repeated prime factors of 39 and 118:
Since there is no common factors between 39 and 118, multiplying the given numbers directly provides the LCM of
39 and 118.
= 39 x 118
= 4602
lcm(39 and 118) = 4602
Hence,
lcm of 39 and 118 is 4602
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 39 and 118.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 39 and 118
What to be found:
lcm (39, 118) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
39 and 118
step 3 Choose the divisor which divides each or most of the given integers (39 and 118), 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 39 and 118 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 39 | 118 |
| 3 | 39 | 59 |
| 13 | 13 | 59 |
| 59 | 1 | 59 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 39 and 118:
= 2 x 3 x 13 x 59
= 4602
LCM(39, 118) = 4602
The LCM of two numbers 39 and 118 is 4602