LCM of 168 and 196
1176 is the LCM of 168 and 196. 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 196, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 168 and 196?
lcm (168 196) = (?)
168 => 2 x 2 x 2 x 3 x 7
196 => 2 x 2 x 7 x 7
= 2 x 2 x 7 x 2 x 3 x 7
= 1176
lcm (168 and 196) = 1176
1176 is the LCM of 168 and 196.
where,
168 is a positive integer,
196 is a positive integer,
1176 is the LCM of 168 and 196,
{2 x 2 x 7} in {2 x 2 x 2 x 3 x 7, 2 x 2 x 7 x 7} are the common factors of 168 and 196,
{2 x 3 x 7} in {2 x 2 x 2 x 3 x 7, 2 x 2 x 7 x 7} are the uncommon factors of 168 and 196.
Use in Mathematics: LCM of 168 and 196
The below are some of the mathematical applications where lcm of 168 and 196 can be used:
- to find the least number which is exactly divisible by 168 and 196.
- to find the common denominator for two fractions having 168 and 196 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 168 and 196 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 196 seconds repeatedly. The answer is that all bells A and B toll together at 1176 seconds for the first time, at 2352 seconds for the second time, at 3528 seconds for the third time and so on.
Important Notes: 168 and 196 lcm
The below are the important notes to be remembered while solving the lcm of 168 and 196:
- The common prime factors and the remaining prime factors of 168 and 196 should be multiplied to find the least common multiple of 168 and 196, when solving lcm by using prime factors method.
- The results of lcm of 168 and 196, and the lcm of 196 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 196?
The below solved example with step by step work shows how to find what is the lcm of 168 and 196 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 168 and 196?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 168
B = 196
What to be found:
find the lcm of 168 and 196
step 2 Find the prime factors of 168 and 196:
Prime factors of 168 = 2 x 2 x 2 x 3 x 7
Prime factors of 196 = 2 x 2 x 7 x 7
step 3 Identify the repeated and non-repeated prime factors of 168 and 196:
{2, 2, 7} are the most repeated factors and {2 x 3 x 7} are the non-repeated factors of 168 and 196.
step 4 Find the product of repeated and non-repeated prime factors of 168 and 196:
= 2 x 2 x 7 x 2 x 3 x 7
= 1176
lcm(168 and 196) = 1176
Hence,
lcm of 168 and 196 is 1176
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 168 and 196.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 168 and 196
What to be found:
lcm (168, 196) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
168 and 196
step 3 Choose the divisor which divides each or most of the given integers (168 and 196), 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 196 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 168 | 196 |
| 2 | 84 | 98 |
| 2 | 42 | 49 |
| 3 | 21 | 49 |
| 7 | 7 | 49 |
| 7 | 1 | 7 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 168 and 196:
= 2 x 2 x 2 x 3 x 7 x 7
= 1176
LCM(168, 196) = 1176
The LCM of two numbers 168 and 196 is 1176