142 and 156 LCM
LCM of 142 and 156 is equal to 11076. The comprehensive work provides more insight of how to find what is the lcm of 142 and 156 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 142 and 156?
lcm (142 156) = (?)
142 => 2 x 71
156 => 2 x 2 x 3 x 13
= 2 x 71 x 2 x 3 x 13
= 11076
lcm (142 and 156) = 11076
11076 is the lcm of 142 and 156.
where,
142 is a positive integer,
156 is a positive integer,
11076 is the lcm of 142 and 156,
{2} in {2 x 71, 2 x 2 x 3 x 13} is the common factors of 142 and 156,
{71 x 2 x 3 x 13} in {2 x 71, 2 x 2 x 3 x 13} are the uncommon factors of 142 and 156.
Use in Mathematics: LCM of 142 and 156
The below are some of the mathematical applications where lcm of 142 and 156 can be used:
- to find the least number which is exactly divisible by 142 and 156.
- to find the common denominator for two fractions having 142 and 156 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 142 and 156 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 156 seconds repeatedly. The answer is that all bells A and B toll together at 11076 seconds for the first time, at 22152 seconds for the second time, at 33228 seconds for the third time and so on.
Important Notes: 142 and 156 lcm
The below are the important notes to be remembered while solving the lcm of 142 and 156:
- The common prime factors and the remaining prime factors of 142 and 156 should be multiplied to find the least common multiple of 142 and 156, when solving lcm by using prime factors method.
- The results of lcm of 142 and 156, and the lcm of 156 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 156?
The below solved example with step by step work shows how to find what is the lcm of 142 and 156 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 142 and 156?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 142
B = 156
What to be found:
find the lcm of 142 and 156
step 2 Find the prime factors of 142 and 156:
Prime factors of 142 = 2 x 71
Prime factors of 156 = 2 x 2 x 3 x 13
step 3 Identify the repeated and non-repeated prime factors of 142 and 156:
{2} is the most repeated factor and {71 x 2 x 3 x 13} are the non-repeated factors of 142 and 156.
step 4 Find the product of repeated and non-repeated prime factors of 142 and 156:
= 2 x 71 x 2 x 3 x 13
= 11076
lcm(142 and 156) = 11076
Hence,
lcm of 142 and 156 is 11076
This special division method is the easiest way to understand the entire calculation of what is the lcm of 142 and 156.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 142 and 156
What to be found:
lcm (142, 156) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
142 and 156
step 3 Choose the divisor which divides each or most of the given integers (142 and 156), 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 156 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 142 | 156 |
| 2 | 71 | 78 |
| 3 | 71 | 39 |
| 13 | 71 | 13 |
| 71 | 71 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 142 and 156:
= 2 x 2 x 3 x 13 x 71
= 11076
LCM(142, 156) = 11076
The least common multiple for two numbers 142 and 156 is 11076