LCM of 42 and 166
3486 is the LCM of 42 and 166. 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 166, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 42 and 166?
lcm (42 166) = (?)
42 => 2 x 3 x 7
166 => 2 x 83
= 2 x 3 x 7 x 83
= 3486
lcm (42 and 166) = 3486
3486 is the LCM of 42 and 166.
where,
42 is a positive integer,
166 is a positive integer,
3486 is the LCM of 42 and 166,
{2} in {2 x 3 x 7, 2 x 83} is the common factors of 42 and 166,
{3 x 7 x 83} in {2 x 3 x 7, 2 x 83} are the uncommon factors of 42 and 166.
Use in Mathematics: LCM of 42 and 166
The below are some of the mathematical applications where lcm of 42 and 166 can be used:
- to find the least number which is exactly divisible by 42 and 166.
- to find the common denominator for two fractions having 42 and 166 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 42 and 166 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 166 seconds repeatedly. The answer is that all bells A and B toll together at 3486 seconds for the first time, at 6972 seconds for the second time, at 10458 seconds for the third time and so on.
Important Notes: 42 and 166 lcm
The below are the important notes to be remembered while solving the lcm of 42 and 166:
- The common prime factors and the remaining prime factors of 42 and 166 should be multiplied to find the least common multiple of 42 and 166, when solving lcm by using prime factors method.
- The results of lcm of 42 and 166, and the lcm of 166 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 166?
The below solved example with step by step work shows how to find what is the lcm of 42 and 166 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 42 and 166?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 42
B = 166
What to be found:
find the lcm of 42 and 166
step 2 Find the prime factors of 42 and 166:
Prime factors of 42 = 2 x 3 x 7
Prime factors of 166 = 2 x 83
step 3 Identify the repeated and non-repeated prime factors of 42 and 166:
{2} is the most repeated factor and {3 x 7 x 83} are the non-repeated factors of 42 and 166.
step 4 Find the product of repeated and non-repeated prime factors of 42 and 166:
= 2 x 3 x 7 x 83
= 3486
lcm(42 and 166) = 3486
Hence,
lcm of 42 and 166 is 3486
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 42 and 166.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 42 and 166
What to be found:
lcm (42, 166) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
42 and 166
step 3 Choose the divisor which divides each or most of the given integers (42 and 166), 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 166 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 42 | 166 |
| 3 | 21 | 83 |
| 7 | 7 | 83 |
| 83 | 1 | 83 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 42 and 166:
= 2 x 3 x 7 x 83
= 3486
LCM(42, 166) = 3486
The LCM of two numbers 42 and 166 is 3486