LCM of 68 and 3
204 is the LCM of 68 and 3. 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 68 and 3, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 68 and 3?
lcm (68 3) = (?)
68 => 2 x 2 x 17
3 => 3
= 2 x 2 x 17 x 3
= 204
lcm (68 and 3) = 204
204 is the LCM of 68 and 3.
where,
68 is a positive integer,
3 is a positive integer,
204 is the LCM of 68 and 3,
There is no common factors of 68 and 3 in {2 x 2 x 17, 3},
{2 x 2 x 17 x 3} in {2 x 2 x 17, 3} are the uncommon factors of 68 and 3.
Use in Mathematics: LCM of 68 and 3
The below are some of the mathematical applications where lcm of 68 and 3 can be used:
- to find the least number which is exactly divisible by 68 and 3.
- to find the common denominator for two fractions having 68 and 3 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 68 and 3 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 68 seconds and bell B tolls at 3 seconds repeatedly. The answer is that all bells A and B toll together at 204 seconds for the first time, at 408 seconds for the second time, at 612 seconds for the third time and so on.
Important Notes: 68 and 3 lcm
The below are the important notes to be remembered while solving the lcm of 68 and 3:
- The common prime factors and the remaining prime factors of 68 and 3 should be multiplied to find the least common multiple of 68 and 3, when solving lcm by using prime factors method.
- The results of lcm of 68 and 3, and the lcm of 3 and 68 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 68 and 3?
The below solved example with step by step work shows how to find what is the lcm of 68 and 3 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 68 and 3?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 68
B = 3
What to be found:
find the lcm of 68 and 3
step 2 Find the prime factors of 68 and 3:
Prime factors of 68 = 2 x 2 x 17
Prime factors of 3 = 3
step 3Identify the repeated and non-repeated prime factors of 68 and 3:
Since there is no common factors between 68 and 3, multiplying the given numbers directly provides the LCM of
68 and 3.
= 68 x 3
= 204
lcm(68 and 3) = 204
Hence,
lcm of 68 and 3 is 204
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 68 and 3.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 68 and 3
What to be found:
lcm (68, 3) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
68 and 3
step 3 Choose the divisor which divides each or most of the given integers (68 and 3), 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 68 and 3 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 68 | 3 |
| 2 | 34 | 3 |
| 3 | 17 | 3 |
| 17 | 17 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 68 and 3:
= 2 x 2 x 3 x 17
= 204
LCM(68, 3) = 204
The LCM of two numbers 68 and 3 is 204