LCM of 178 and 360
32040 is the LCM of 178 and 360. 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 178 and 360, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 178 and 360?
lcm (178 360) = (?)
178 => 2 x 89
360 => 2 x 2 x 2 x 3 x 3 x 5
= 2 x 89 x 2 x 2 x 3 x 3 x 5
= 32040
lcm (178 and 360) = 32040
32040 is the LCM of 178 and 360.
where,
178 is a positive integer,
360 is a positive integer,
32040 is the LCM of 178 and 360,
{2} in {2 x 89, 2 x 2 x 2 x 3 x 3 x 5} is the common factors of 178 and 360,
{89 x 2 x 2 x 3 x 3 x 5} in {2 x 89, 2 x 2 x 2 x 3 x 3 x 5} are the uncommon factors of 178 and 360.
Use in Mathematics: LCM of 178 and 360
The below are some of the mathematical applications where lcm of 178 and 360 can be used:
- to find the least number which is exactly divisible by 178 and 360.
- to find the common denominator for two fractions having 178 and 360 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 178 and 360 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 178 seconds and bell B tolls at 360 seconds repeatedly. The answer is that all bells A and B toll together at 32040 seconds for the first time, at 64080 seconds for the second time, at 96120 seconds for the third time and so on.
Important Notes: 178 and 360 lcm
The below are the important notes to be remembered while solving the lcm of 178 and 360:
- The common prime factors and the remaining prime factors of 178 and 360 should be multiplied to find the least common multiple of 178 and 360, when solving lcm by using prime factors method.
- The results of lcm of 178 and 360, and the lcm of 360 and 178 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 178 and 360?
The below solved example with step by step work shows how to find what is the lcm of 178 and 360 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 178 and 360?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 178
B = 360
What to be found:
find the lcm of 178 and 360
step 2 Find the prime factors of 178 and 360:
Prime factors of 178 = 2 x 89
Prime factors of 360 = 2 x 2 x 2 x 3 x 3 x 5
step 3 Identify the repeated and non-repeated prime factors of 178 and 360:
{2} is the most repeated factor and {89 x 2 x 2 x 3 x 3 x 5} are the non-repeated factors of 178 and 360.
step 4 Find the product of repeated and non-repeated prime factors of 178 and 360:
= 2 x 89 x 2 x 2 x 3 x 3 x 5
= 32040
lcm(178 and 360) = 32040
Hence,
lcm of 178 and 360 is 32040
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 178 and 360.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 178 and 360
What to be found:
lcm (178, 360) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
178 and 360
step 3 Choose the divisor which divides each or most of the given integers (178 and 360), 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 178 and 360 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 178 | 360 |
| 2 | 89 | 180 |
| 2 | 89 | 90 |
| 3 | 89 | 45 |
| 3 | 89 | 15 |
| 5 | 89 | 5 |
| 89 | 89 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 178 and 360:
= 2 x 2 x 2 x 3 x 3 x 5 x 89
= 32040
LCM(178, 360) = 32040
The LCM of two numbers 178 and 360 is 32040