LCM of 13 and 42
546 is the LCM of 13 and 42. 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 13 and 42, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 13 and 42?
lcm (13 42) = (?)
13 => 13
42 => 2 x 3 x 7
= 13 x 2 x 3 x 7
= 546
lcm (13 and 42) = 546
546 is the LCM of 13 and 42.
where,
13 is a positive integer,
42 is a positive integer,
546 is the LCM of 13 and 42,
There is no common factors of 13 and 42 in {13, 2 x 3 x 7},
{13 x 2 x 3 x 7} in {13, 2 x 3 x 7} are the uncommon factors of 13 and 42.
Use in Mathematics: LCM of 13 and 42
The below are some of the mathematical applications where lcm of 13 and 42 can be used:
- to find the least number which is exactly divisible by 13 and 42.
- to find the common denominator for two fractions having 13 and 42 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 13 and 42 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 13 seconds and bell B tolls at 42 seconds repeatedly. The answer is that all bells A and B toll together at 546 seconds for the first time, at 1092 seconds for the second time, at 1638 seconds for the third time and so on.
Important Notes: 13 and 42 lcm
The below are the important notes to be remembered while solving the lcm of 13 and 42:
- The common prime factors and the remaining prime factors of 13 and 42 should be multiplied to find the least common multiple of 13 and 42, when solving lcm by using prime factors method.
- The results of lcm of 13 and 42, and the lcm of 42 and 13 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 13 and 42?
The below solved example with step by step work shows how to find what is the lcm of 13 and 42 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 13 and 42?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 13
B = 42
What to be found:
find the lcm of 13 and 42
step 2 Find the prime factors of 13 and 42:
Prime factors of 13 = 13
Prime factors of 42 = 2 x 3 x 7
step 3Identify the repeated and non-repeated prime factors of 13 and 42:
Since there is no common factors between 13 and 42, multiplying the given numbers directly provides the LCM of
13 and 42.
= 13 x 42
= 546
lcm(13 and 42) = 546
Hence,
lcm of 13 and 42 is 546
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 13 and 42.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 13 and 42
What to be found:
lcm (13, 42) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
13 and 42
step 3 Choose the divisor which divides each or most of the given integers (13 and 42), 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 13 and 42 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 13 | 42 |
| 3 | 13 | 21 |
| 7 | 13 | 7 |
| 13 | 13 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 13 and 42:
= 2 x 3 x 7 x 13
= 546
LCM(13, 42) = 546
The LCM of two numbers 13 and 42 is 546