LCM of 180 and 295
10620 is the LCM of 180 and 295. 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 180 and 295, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 180 and 295?
lcm (180 295) = (?)
180 => 2 x 2 x 3 x 3 x 5
295 => 5 x 59
= 5 x 2 x 2 x 3 x 3 x 59
= 10620
lcm (180 and 295) = 10620
10620 is the LCM of 180 and 295.
where,
180 is a positive integer,
295 is a positive integer,
10620 is the LCM of 180 and 295,
{5} in {2 x 2 x 3 x 3 x 5, 5 x 59} is the common factors of 180 and 295,
{2 x 2 x 3 x 3 x 59} in {2 x 2 x 3 x 3 x 5, 5 x 59} are the uncommon factors of 180 and 295.
Use in Mathematics: LCM of 180 and 295
The below are some of the mathematical applications where lcm of 180 and 295 can be used:
- to find the least number which is exactly divisible by 180 and 295.
- to find the common denominator for two fractions having 180 and 295 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 180 and 295 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 180 seconds and bell B tolls at 295 seconds repeatedly. The answer is that all bells A and B toll together at 10620 seconds for the first time, at 21240 seconds for the second time, at 31860 seconds for the third time and so on.
Important Notes: 180 and 295 lcm
The below are the important notes to be remembered while solving the lcm of 180 and 295:
- The common prime factors and the remaining prime factors of 180 and 295 should be multiplied to find the least common multiple of 180 and 295, when solving lcm by using prime factors method.
- The results of lcm of 180 and 295, and the lcm of 295 and 180 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 180 and 295?
The below solved example with step by step work shows how to find what is the lcm of 180 and 295 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 180 and 295?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 180
B = 295
What to be found:
find the lcm of 180 and 295
step 2 Find the prime factors of 180 and 295:
Prime factors of 180 = 2 x 2 x 3 x 3 x 5
Prime factors of 295 = 5 x 59
step 3 Identify the repeated and non-repeated prime factors of 180 and 295:
{5} is the most repeated factor and {2 x 2 x 3 x 3 x 59} are the non-repeated factors of 180 and 295.
step 4 Find the product of repeated and non-repeated prime factors of 180 and 295:
= 5 x 2 x 2 x 3 x 3 x 59
= 10620
lcm(180 and 295) = 10620
Hence,
lcm of 180 and 295 is 10620
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 180 and 295.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 180 and 295
What to be found:
lcm (180, 295) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
180 and 295
step 3 Choose the divisor which divides each or most of the given integers (180 and 295), 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 180 and 295 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 180 | 295 |
| 2 | 90 | 295 |
| 3 | 45 | 295 |
| 3 | 15 | 295 |
| 5 | 5 | 295 |
| 59 | 1 | 59 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 180 and 295:
= 2 x 2 x 3 x 3 x 5 x 59
= 10620
LCM(180, 295) = 10620
The LCM of two numbers 180 and 295 is 10620