LCM of 178 and 326
29014 is the LCM of 178 and 326. 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 326, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 178 and 326?
lcm (178 326) = (?)
178 => 2 x 89
326 => 2 x 163
= 2 x 89 x 163
= 29014
lcm (178 and 326) = 29014
29014 is the LCM of 178 and 326.
where,
178 is a positive integer,
326 is a positive integer,
29014 is the LCM of 178 and 326,
{2} in {2 x 89, 2 x 163} is the common factors of 178 and 326,
{89 x 163} in {2 x 89, 2 x 163} are the uncommon factors of 178 and 326.
Use in Mathematics: LCM of 178 and 326
The below are some of the mathematical applications where lcm of 178 and 326 can be used:
- to find the least number which is exactly divisible by 178 and 326.
- to find the common denominator for two fractions having 178 and 326 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 178 and 326 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 326 seconds repeatedly. The answer is that all bells A and B toll together at 29014 seconds for the first time, at 58028 seconds for the second time, at 87042 seconds for the third time and so on.
Important Notes: 178 and 326 lcm
The below are the important notes to be remembered while solving the lcm of 178 and 326:
- The common prime factors and the remaining prime factors of 178 and 326 should be multiplied to find the least common multiple of 178 and 326, when solving lcm by using prime factors method.
- The results of lcm of 178 and 326, and the lcm of 326 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 326?
The below solved example with step by step work shows how to find what is the lcm of 178 and 326 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 178 and 326?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 178
B = 326
What to be found:
find the lcm of 178 and 326
step 2 Find the prime factors of 178 and 326:
Prime factors of 178 = 2 x 89
Prime factors of 326 = 2 x 163
step 3 Identify the repeated and non-repeated prime factors of 178 and 326:
{2} is the most repeated factor and {89 x 163} are the non-repeated factors of 178 and 326.
step 4 Find the product of repeated and non-repeated prime factors of 178 and 326:
= 2 x 89 x 163
= 29014
lcm(178 and 326) = 29014
Hence,
lcm of 178 and 326 is 29014
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 178 and 326.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 178 and 326
What to be found:
lcm (178, 326) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
178 and 326
step 3 Choose the divisor which divides each or most of the given integers (178 and 326), 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 326 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 178 | 326 |
| 89 | 89 | 163 |
| 163 | 1 | 163 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 178 and 326:
= 2 x 89 x 163
= 29014
LCM(178, 326) = 29014
The LCM of two numbers 178 and 326 is 29014