LCM of 21 and 305
6405 is the LCM of 21 and 305. 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 21 and 305, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 21 and 305?
lcm (21 305) = (?)
21 => 3 x 7
305 => 5 x 61
= 3 x 7 x 5 x 61
= 6405
lcm (21 and 305) = 6405
6405 is the LCM of 21 and 305.
where,
21 is a positive integer,
305 is a positive integer,
6405 is the LCM of 21 and 305,
There is no common factors of 21 and 305 in {3 x 7, 5 x 61},
{3 x 7 x 5 x 61} in {3 x 7, 5 x 61} are the uncommon factors of 21 and 305.
Use in Mathematics: LCM of 21 and 305
The below are some of the mathematical applications where lcm of 21 and 305 can be used:
- to find the least number which is exactly divisible by 21 and 305.
- to find the common denominator for two fractions having 21 and 305 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 21 and 305 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 21 seconds and bell B tolls at 305 seconds repeatedly. The answer is that all bells A and B toll together at 6405 seconds for the first time, at 12810 seconds for the second time, at 19215 seconds for the third time and so on.
Important Notes: 21 and 305 lcm
The below are the important notes to be remembered while solving the lcm of 21 and 305:
- The common prime factors and the remaining prime factors of 21 and 305 should be multiplied to find the least common multiple of 21 and 305, when solving lcm by using prime factors method.
- The results of lcm of 21 and 305, and the lcm of 305 and 21 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 21 and 305?
The below solved example with step by step work shows how to find what is the lcm of 21 and 305 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 21 and 305?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 21
B = 305
What to be found:
find the lcm of 21 and 305
step 2 Find the prime factors of 21 and 305:
Prime factors of 21 = 3 x 7
Prime factors of 305 = 5 x 61
step 3Identify the repeated and non-repeated prime factors of 21 and 305:
Since there is no common factors between 21 and 305, multiplying the given numbers directly provides the LCM of
21 and 305.
= 21 x 305
= 6405
lcm(21 and 305) = 6405
Hence,
lcm of 21 and 305 is 6405
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 21 and 305.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 21 and 305
What to be found:
lcm (21, 305) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
21 and 305
step 3 Choose the divisor which divides each or most of the given integers (21 and 305), 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 21 and 305 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 21 | 305 |
| 5 | 7 | 305 |
| 7 | 7 | 61 |
| 61 | 1 | 61 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 21 and 305:
= 3 x 5 x 7 x 61
= 6405
LCM(21, 305) = 6405
The LCM of two numbers 21 and 305 is 6405