LCM of 69 and 300
6900 is the LCM of 69 and 300. 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 69 and 300, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 69 and 300?
lcm (69 300) = (?)
69 => 3 x 23
300 => 2 x 2 x 3 x 5 x 5
= 3 x 23 x 2 x 2 x 5 x 5
= 6900
lcm (69 and 300) = 6900
6900 is the LCM of 69 and 300.
where,
69 is a positive integer,
300 is a positive integer,
6900 is the LCM of 69 and 300,
{3} in {3 x 23, 2 x 2 x 3 x 5 x 5} is the common factors of 69 and 300,
{23 x 2 x 2 x 5 x 5} in {3 x 23, 2 x 2 x 3 x 5 x 5} are the uncommon factors of 69 and 300.
Use in Mathematics: LCM of 69 and 300
The below are some of the mathematical applications where lcm of 69 and 300 can be used:
- to find the least number which is exactly divisible by 69 and 300.
- to find the common denominator for two fractions having 69 and 300 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 69 and 300 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 69 seconds and bell B tolls at 300 seconds repeatedly. The answer is that all bells A and B toll together at 6900 seconds for the first time, at 13800 seconds for the second time, at 20700 seconds for the third time and so on.
Important Notes: 69 and 300 lcm
The below are the important notes to be remembered while solving the lcm of 69 and 300:
- The common prime factors and the remaining prime factors of 69 and 300 should be multiplied to find the least common multiple of 69 and 300, when solving lcm by using prime factors method.
- The results of lcm of 69 and 300, and the lcm of 300 and 69 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 69 and 300?
The below solved example with step by step work shows how to find what is the lcm of 69 and 300 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 69 and 300?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 69
B = 300
What to be found:
find the lcm of 69 and 300
step 2 Find the prime factors of 69 and 300:
Prime factors of 69 = 3 x 23
Prime factors of 300 = 2 x 2 x 3 x 5 x 5
step 3 Identify the repeated and non-repeated prime factors of 69 and 300:
{3} is the most repeated factor and {23 x 2 x 2 x 5 x 5} are the non-repeated factors of 69 and 300.
step 4 Find the product of repeated and non-repeated prime factors of 69 and 300:
= 3 x 23 x 2 x 2 x 5 x 5
= 6900
lcm(69 and 300) = 6900
Hence,
lcm of 69 and 300 is 6900
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 69 and 300.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 69 and 300
What to be found:
lcm (69, 300) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
69 and 300
step 3 Choose the divisor which divides each or most of the given integers (69 and 300), 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 69 and 300 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 69 | 300 |
| 2 | 69 | 150 |
| 3 | 69 | 75 |
| 5 | 23 | 25 |
| 5 | 23 | 5 |
| 23 | 23 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 69 and 300:
= 2 x 2 x 3 x 5 x 5 x 23
= 6900
LCM(69, 300) = 6900
The LCM of two numbers 69 and 300 is 6900