LCM of 168 and 358
30072 is the LCM of 168 and 358. 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 168 and 358, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 168 and 358?
lcm (168 358) = (?)
168 => 2 x 2 x 2 x 3 x 7
358 => 2 x 179
= 2 x 2 x 2 x 3 x 7 x 179
= 30072
lcm (168 and 358) = 30072
30072 is the LCM of 168 and 358.
where,
168 is a positive integer,
358 is a positive integer,
30072 is the LCM of 168 and 358,
{2} in {2 x 2 x 2 x 3 x 7, 2 x 179} is the common factors of 168 and 358,
{2 x 2 x 3 x 7 x 179} in {2 x 2 x 2 x 3 x 7, 2 x 179} are the uncommon factors of 168 and 358.
Use in Mathematics: LCM of 168 and 358
The below are some of the mathematical applications where lcm of 168 and 358 can be used:
- to find the least number which is exactly divisible by 168 and 358.
- to find the common denominator for two fractions having 168 and 358 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 168 and 358 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 168 seconds and bell B tolls at 358 seconds repeatedly. The answer is that all bells A and B toll together at 30072 seconds for the first time, at 60144 seconds for the second time, at 90216 seconds for the third time and so on.
Important Notes: 168 and 358 lcm
The below are the important notes to be remembered while solving the lcm of 168 and 358:
- The common prime factors and the remaining prime factors of 168 and 358 should be multiplied to find the least common multiple of 168 and 358, when solving lcm by using prime factors method.
- The results of lcm of 168 and 358, and the lcm of 358 and 168 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 168 and 358?
The below solved example with step by step work shows how to find what is the lcm of 168 and 358 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 168 and 358?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 168
B = 358
What to be found:
find the lcm of 168 and 358
step 2 Find the prime factors of 168 and 358:
Prime factors of 168 = 2 x 2 x 2 x 3 x 7
Prime factors of 358 = 2 x 179
step 3 Identify the repeated and non-repeated prime factors of 168 and 358:
{2} is the most repeated factor and {2 x 2 x 3 x 7 x 179} are the non-repeated factors of 168 and 358.
step 4 Find the product of repeated and non-repeated prime factors of 168 and 358:
= 2 x 2 x 2 x 3 x 7 x 179
= 30072
lcm(168 and 358) = 30072
Hence,
lcm of 168 and 358 is 30072
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 168 and 358.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 168 and 358
What to be found:
lcm (168, 358) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
168 and 358
step 3 Choose the divisor which divides each or most of the given integers (168 and 358), 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 168 and 358 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 168 | 358 |
| 2 | 84 | 179 |
| 2 | 42 | 179 |
| 3 | 21 | 179 |
| 7 | 7 | 179 |
| 179 | 1 | 179 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 168 and 358:
= 2 x 2 x 2 x 3 x 7 x 179
= 30072
LCM(168, 358) = 30072
The LCM of two numbers 168 and 358 is 30072