LCM of 9 and 69
207 is the LCM of 9 and 69. 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 9 and 69, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 9 and 69?
lcm (9 69) = (?)
9 => 3 x 3
69 => 3 x 23
= 3 x 3 x 23
= 207
lcm (9 and 69) = 207
207 is the LCM of 9 and 69.
where,
9 is a positive integer,
69 is a positive integer,
207 is the LCM of 9 and 69,
{3} in {3 x 3, 3 x 23} is the common factors of 9 and 69,
{3 x 23} in {3 x 3, 3 x 23} are the uncommon factors of 9 and 69.
Use in Mathematics: LCM of 9 and 69
The below are some of the mathematical applications where lcm of 9 and 69 can be used:
- to find the least number which is exactly divisible by 9 and 69.
- to find the common denominator for two fractions having 9 and 69 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 9 and 69 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 9 seconds and bell B tolls at 69 seconds repeatedly. The answer is that all bells A and B toll together at 207 seconds for the first time, at 414 seconds for the second time, at 621 seconds for the third time and so on.
Important Notes: 9 and 69 lcm
The below are the important notes to be remembered while solving the lcm of 9 and 69:
- The common prime factors and the remaining prime factors of 9 and 69 should be multiplied to find the least common multiple of 9 and 69, when solving lcm by using prime factors method.
- The results of lcm of 9 and 69, and the lcm of 69 and 9 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 9 and 69?
The below solved example with step by step work shows how to find what is the lcm of 9 and 69 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 9 and 69?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 9
B = 69
What to be found:
find the lcm of 9 and 69
step 2 Find the prime factors of 9 and 69:
Prime factors of 9 = 3 x 3
Prime factors of 69 = 3 x 23
step 3 Identify the repeated and non-repeated prime factors of 9 and 69:
{3} is the most repeated factor and {3 x 23} are the non-repeated factors of 9 and 69.
step 4 Find the product of repeated and non-repeated prime factors of 9 and 69:
= 3 x 3 x 23
= 207
lcm(9 and 69) = 207
Hence,
lcm of 9 and 69 is 207
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 9 and 69.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 9 and 69
What to be found:
lcm (9, 69) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
9 and 69
step 3 Choose the divisor which divides each or most of the given integers (9 and 69), 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 9 and 69 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 9 | 69 |
| 3 | 3 | 23 |
| 23 | 1 | 23 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 9 and 69:
= 3 x 3 x 23
= 207
LCM(9, 69) = 207
The LCM of two numbers 9 and 69 is 207