LCM of 158 and 180
14220 is the LCM of 158 and 180. 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 158 and 180, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 158 and 180?
lcm (158 180) = (?)
158 => 2 x 79
180 => 2 x 2 x 3 x 3 x 5
= 2 x 79 x 2 x 3 x 3 x 5
= 14220
lcm (158 and 180) = 14220
14220 is the LCM of 158 and 180.
where,
158 is a positive integer,
180 is a positive integer,
14220 is the LCM of 158 and 180,
{2} in {2 x 79, 2 x 2 x 3 x 3 x 5} is the common factors of 158 and 180,
{79 x 2 x 3 x 3 x 5} in {2 x 79, 2 x 2 x 3 x 3 x 5} are the uncommon factors of 158 and 180.
Use in Mathematics: LCM of 158 and 180
The below are some of the mathematical applications where lcm of 158 and 180 can be used:
- to find the least number which is exactly divisible by 158 and 180.
- to find the common denominator for two fractions having 158 and 180 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 158 and 180 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 158 seconds and bell B tolls at 180 seconds repeatedly. The answer is that all bells A and B toll together at 14220 seconds for the first time, at 28440 seconds for the second time, at 42660 seconds for the third time and so on.
Important Notes: 158 and 180 lcm
The below are the important notes to be remembered while solving the lcm of 158 and 180:
- The common prime factors and the remaining prime factors of 158 and 180 should be multiplied to find the least common multiple of 158 and 180, when solving lcm by using prime factors method.
- The results of lcm of 158 and 180, and the lcm of 180 and 158 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 158 and 180?
The below solved example with step by step work shows how to find what is the lcm of 158 and 180 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 158 and 180?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 158
B = 180
What to be found:
find the lcm of 158 and 180
step 2 Find the prime factors of 158 and 180:
Prime factors of 158 = 2 x 79
Prime factors of 180 = 2 x 2 x 3 x 3 x 5
step 3 Identify the repeated and non-repeated prime factors of 158 and 180:
{2} is the most repeated factor and {79 x 2 x 3 x 3 x 5} are the non-repeated factors of 158 and 180.
step 4 Find the product of repeated and non-repeated prime factors of 158 and 180:
= 2 x 79 x 2 x 3 x 3 x 5
= 14220
lcm(158 and 180) = 14220
Hence,
lcm of 158 and 180 is 14220
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 158 and 180.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 158 and 180
What to be found:
lcm (158, 180) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
158 and 180
step 3 Choose the divisor which divides each or most of the given integers (158 and 180), 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 158 and 180 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 158 | 180 |
| 2 | 79 | 90 |
| 3 | 79 | 45 |
| 3 | 79 | 15 |
| 5 | 79 | 5 |
| 79 | 79 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 158 and 180:
= 2 x 2 x 3 x 3 x 5 x 79
= 14220
LCM(158, 180) = 14220
The LCM of two numbers 158 and 180 is 14220