LCM of 156 and 171
8892 is the LCM of 156 and 171. 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 156 and 171, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 156 and 171?
lcm (156 171) = (?)
156 => 2 x 2 x 3 x 13
171 => 3 x 3 x 19
= 3 x 2 x 2 x 13 x 3 x 19
= 8892
lcm (156 and 171) = 8892
8892 is the LCM of 156 and 171.
where,
156 is a positive integer,
171 is a positive integer,
8892 is the LCM of 156 and 171,
{3} in {2 x 2 x 3 x 13, 3 x 3 x 19} is the common factors of 156 and 171,
{2 x 2 x 13 x 3 x 19} in {2 x 2 x 3 x 13, 3 x 3 x 19} are the uncommon factors of 156 and 171.
Use in Mathematics: LCM of 156 and 171
The below are some of the mathematical applications where lcm of 156 and 171 can be used:
- to find the least number which is exactly divisible by 156 and 171.
- to find the common denominator for two fractions having 156 and 171 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 156 and 171 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 156 seconds and bell B tolls at 171 seconds repeatedly. The answer is that all bells A and B toll together at 8892 seconds for the first time, at 17784 seconds for the second time, at 26676 seconds for the third time and so on.
Important Notes: 156 and 171 lcm
The below are the important notes to be remembered while solving the lcm of 156 and 171:
- The common prime factors and the remaining prime factors of 156 and 171 should be multiplied to find the least common multiple of 156 and 171, when solving lcm by using prime factors method.
- The results of lcm of 156 and 171, and the lcm of 171 and 156 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 156 and 171?
The below solved example with step by step work shows how to find what is the lcm of 156 and 171 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 156 and 171?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 156
B = 171
What to be found:
find the lcm of 156 and 171
step 2 Find the prime factors of 156 and 171:
Prime factors of 156 = 2 x 2 x 3 x 13
Prime factors of 171 = 3 x 3 x 19
step 3 Identify the repeated and non-repeated prime factors of 156 and 171:
{3} is the most repeated factor and {2 x 2 x 13 x 3 x 19} are the non-repeated factors of 156 and 171.
step 4 Find the product of repeated and non-repeated prime factors of 156 and 171:
= 3 x 2 x 2 x 13 x 3 x 19
= 8892
lcm(156 and 171) = 8892
Hence,
lcm of 156 and 171 is 8892
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 156 and 171.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 156 and 171
What to be found:
lcm (156, 171) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
156 and 171
step 3 Choose the divisor which divides each or most of the given integers (156 and 171), 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 156 and 171 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 156 | 171 |
| 2 | 78 | 171 |
| 3 | 39 | 171 |
| 3 | 13 | 57 |
| 13 | 13 | 19 |
| 19 | 1 | 19 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 156 and 171:
= 2 x 2 x 3 x 3 x 13 x 19
= 8892
LCM(156, 171) = 8892
The LCM of two numbers 156 and 171 is 8892