LCM of 9 and 219
657 is the LCM of 9 and 219. 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 219, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 9 and 219?
lcm (9 219) = (?)
9 => 3 x 3
219 => 3 x 73
= 3 x 3 x 73
= 657
lcm (9 and 219) = 657
657 is the LCM of 9 and 219.
where,
9 is a positive integer,
219 is a positive integer,
657 is the LCM of 9 and 219,
{3} in {3 x 3, 3 x 73} is the common factors of 9 and 219,
{3 x 73} in {3 x 3, 3 x 73} are the uncommon factors of 9 and 219.
Use in Mathematics: LCM of 9 and 219
The below are some of the mathematical applications where lcm of 9 and 219 can be used:
- to find the least number which is exactly divisible by 9 and 219.
- to find the common denominator for two fractions having 9 and 219 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 9 and 219 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 219 seconds repeatedly. The answer is that all bells A and B toll together at 657 seconds for the first time, at 1314 seconds for the second time, at 1971 seconds for the third time and so on.
Important Notes: 9 and 219 lcm
The below are the important notes to be remembered while solving the lcm of 9 and 219:
- The common prime factors and the remaining prime factors of 9 and 219 should be multiplied to find the least common multiple of 9 and 219, when solving lcm by using prime factors method.
- The results of lcm of 9 and 219, and the lcm of 219 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 219?
The below solved example with step by step work shows how to find what is the lcm of 9 and 219 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 9 and 219?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 9
B = 219
What to be found:
find the lcm of 9 and 219
step 2 Find the prime factors of 9 and 219:
Prime factors of 9 = 3 x 3
Prime factors of 219 = 3 x 73
step 3 Identify the repeated and non-repeated prime factors of 9 and 219:
{3} is the most repeated factor and {3 x 73} are the non-repeated factors of 9 and 219.
step 4 Find the product of repeated and non-repeated prime factors of 9 and 219:
= 3 x 3 x 73
= 657
lcm(9 and 219) = 657
Hence,
lcm of 9 and 219 is 657
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 9 and 219.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 9 and 219
What to be found:
lcm (9, 219) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
9 and 219
step 3 Choose the divisor which divides each or most of the given integers (9 and 219), 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 219 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 9 | 219 |
| 3 | 3 | 73 |
| 73 | 1 | 73 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 9 and 219:
= 3 x 3 x 73
= 657
LCM(9, 219) = 657
The LCM of two numbers 9 and 219 is 657