LCM of 142 and 186
13206 is the LCM of 142 and 186. 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 142 and 186, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 142 and 186?
lcm (142 186) = (?)
142 => 2 x 71
186 => 2 x 3 x 31
= 2 x 71 x 3 x 31
= 13206
lcm (142 and 186) = 13206
13206 is the LCM of 142 and 186.
where,
142 is a positive integer,
186 is a positive integer,
13206 is the LCM of 142 and 186,
{2} in {2 x 71, 2 x 3 x 31} is the common factors of 142 and 186,
{71 x 3 x 31} in {2 x 71, 2 x 3 x 31} are the uncommon factors of 142 and 186.
Use in Mathematics: LCM of 142 and 186
The below are some of the mathematical applications where lcm of 142 and 186 can be used:
- to find the least number which is exactly divisible by 142 and 186.
- to find the common denominator for two fractions having 142 and 186 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 142 and 186 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 142 seconds and bell B tolls at 186 seconds repeatedly. The answer is that all bells A and B toll together at 13206 seconds for the first time, at 26412 seconds for the second time, at 39618 seconds for the third time and so on.
Important Notes: 142 and 186 lcm
The below are the important notes to be remembered while solving the lcm of 142 and 186:
- The common prime factors and the remaining prime factors of 142 and 186 should be multiplied to find the least common multiple of 142 and 186, when solving lcm by using prime factors method.
- The results of lcm of 142 and 186, and the lcm of 186 and 142 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 142 and 186?
The below solved example with step by step work shows how to find what is the lcm of 142 and 186 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 142 and 186?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 142
B = 186
What to be found:
find the lcm of 142 and 186
step 2 Find the prime factors of 142 and 186:
Prime factors of 142 = 2 x 71
Prime factors of 186 = 2 x 3 x 31
step 3 Identify the repeated and non-repeated prime factors of 142 and 186:
{2} is the most repeated factor and {71 x 3 x 31} are the non-repeated factors of 142 and 186.
step 4 Find the product of repeated and non-repeated prime factors of 142 and 186:
= 2 x 71 x 3 x 31
= 13206
lcm(142 and 186) = 13206
Hence,
lcm of 142 and 186 is 13206
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 142 and 186.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 142 and 186
What to be found:
lcm (142, 186) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
142 and 186
step 3 Choose the divisor which divides each or most of the given integers (142 and 186), 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 142 and 186 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 142 | 186 |
| 3 | 71 | 93 |
| 31 | 71 | 31 |
| 71 | 71 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 142 and 186:
= 2 x 3 x 31 x 71
= 13206
LCM(142, 186) = 13206
The LCM of two numbers 142 and 186 is 13206