LCM of 42 and 314
6594 is the LCM of 42 and 314. 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 42 and 314, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 42 and 314?
lcm (42 314) = (?)
42 => 2 x 3 x 7
314 => 2 x 157
= 2 x 3 x 7 x 157
= 6594
lcm (42 and 314) = 6594
6594 is the LCM of 42 and 314.
where,
42 is a positive integer,
314 is a positive integer,
6594 is the LCM of 42 and 314,
{2} in {2 x 3 x 7, 2 x 157} is the common factors of 42 and 314,
{3 x 7 x 157} in {2 x 3 x 7, 2 x 157} are the uncommon factors of 42 and 314.
Use in Mathematics: LCM of 42 and 314
The below are some of the mathematical applications where lcm of 42 and 314 can be used:
- to find the least number which is exactly divisible by 42 and 314.
- to find the common denominator for two fractions having 42 and 314 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 42 and 314 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 42 seconds and bell B tolls at 314 seconds repeatedly. The answer is that all bells A and B toll together at 6594 seconds for the first time, at 13188 seconds for the second time, at 19782 seconds for the third time and so on.
Important Notes: 42 and 314 lcm
The below are the important notes to be remembered while solving the lcm of 42 and 314:
- The common prime factors and the remaining prime factors of 42 and 314 should be multiplied to find the least common multiple of 42 and 314, when solving lcm by using prime factors method.
- The results of lcm of 42 and 314, and the lcm of 314 and 42 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 42 and 314?
The below solved example with step by step work shows how to find what is the lcm of 42 and 314 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 42 and 314?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 42
B = 314
What to be found:
find the lcm of 42 and 314
step 2 Find the prime factors of 42 and 314:
Prime factors of 42 = 2 x 3 x 7
Prime factors of 314 = 2 x 157
step 3 Identify the repeated and non-repeated prime factors of 42 and 314:
{2} is the most repeated factor and {3 x 7 x 157} are the non-repeated factors of 42 and 314.
step 4 Find the product of repeated and non-repeated prime factors of 42 and 314:
= 2 x 3 x 7 x 157
= 6594
lcm(42 and 314) = 6594
Hence,
lcm of 42 and 314 is 6594
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 42 and 314.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 42 and 314
What to be found:
lcm (42, 314) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
42 and 314
step 3 Choose the divisor which divides each or most of the given integers (42 and 314), 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 42 and 314 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 42 | 314 |
| 3 | 21 | 157 |
| 7 | 7 | 157 |
| 157 | 1 | 157 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 42 and 314:
= 2 x 3 x 7 x 157
= 6594
LCM(42, 314) = 6594
The LCM of two numbers 42 and 314 is 6594