LCM of 219 and 303
22119 is the LCM of 219 and 303. 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 219 and 303, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 219 and 303?
lcm (219 303) = (?)
219 => 3 x 73
303 => 3 x 101
= 3 x 73 x 101
= 22119
lcm (219 and 303) = 22119
22119 is the LCM of 219 and 303.
where,
219 is a positive integer,
303 is a positive integer,
22119 is the LCM of 219 and 303,
{3} in {3 x 73, 3 x 101} is the common factors of 219 and 303,
{73 x 101} in {3 x 73, 3 x 101} are the uncommon factors of 219 and 303.
Use in Mathematics: LCM of 219 and 303
The below are some of the mathematical applications where lcm of 219 and 303 can be used:
- to find the least number which is exactly divisible by 219 and 303.
- to find the common denominator for two fractions having 219 and 303 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 219 and 303 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 219 seconds and bell B tolls at 303 seconds repeatedly. The answer is that all bells A and B toll together at 22119 seconds for the first time, at 44238 seconds for the second time, at 66357 seconds for the third time and so on.
Important Notes: 219 and 303 lcm
The below are the important notes to be remembered while solving the lcm of 219 and 303:
- The common prime factors and the remaining prime factors of 219 and 303 should be multiplied to find the least common multiple of 219 and 303, when solving lcm by using prime factors method.
- The results of lcm of 219 and 303, and the lcm of 303 and 219 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 219 and 303?
The below solved example with step by step work shows how to find what is the lcm of 219 and 303 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 219 and 303?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 219
B = 303
What to be found:
find the lcm of 219 and 303
step 2 Find the prime factors of 219 and 303:
Prime factors of 219 = 3 x 73
Prime factors of 303 = 3 x 101
step 3 Identify the repeated and non-repeated prime factors of 219 and 303:
{3} is the most repeated factor and {73 x 101} are the non-repeated factors of 219 and 303.
step 4 Find the product of repeated and non-repeated prime factors of 219 and 303:
= 3 x 73 x 101
= 22119
lcm(219 and 303) = 22119
Hence,
lcm of 219 and 303 is 22119
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 219 and 303.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 219 and 303
What to be found:
lcm (219, 303) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
219 and 303
step 3 Choose the divisor which divides each or most of the given integers (219 and 303), 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 219 and 303 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 219 | 303 |
| 73 | 73 | 101 |
| 101 | 1 | 101 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 219 and 303:
= 3 x 73 x 101
= 22119
LCM(219, 303) = 22119
The LCM of two numbers 219 and 303 is 22119