LCM of 218 and 329
71722 is the LCM of 218 and 329. 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 218 and 329, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 218 and 329?
lcm (218 329) = (?)
218 => 2 x 109
329 => 7 x 47
= 2 x 109 x 7 x 47
= 71722
lcm (218 and 329) = 71722
71722 is the LCM of 218 and 329.
where,
218 is a positive integer,
329 is a positive integer,
71722 is the LCM of 218 and 329,
There is no common factors of 218 and 329 in {2 x 109, 7 x 47},
{2 x 109 x 7 x 47} in {2 x 109, 7 x 47} are the uncommon factors of 218 and 329.
Use in Mathematics: LCM of 218 and 329
The below are some of the mathematical applications where lcm of 218 and 329 can be used:
- to find the least number which is exactly divisible by 218 and 329.
- to find the common denominator for two fractions having 218 and 329 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 218 and 329 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 218 seconds and bell B tolls at 329 seconds repeatedly. The answer is that all bells A and B toll together at 71722 seconds for the first time, at 143444 seconds for the second time, at 215166 seconds for the third time and so on.
Important Notes: 218 and 329 lcm
The below are the important notes to be remembered while solving the lcm of 218 and 329:
- The common prime factors and the remaining prime factors of 218 and 329 should be multiplied to find the least common multiple of 218 and 329, when solving lcm by using prime factors method.
- The results of lcm of 218 and 329, and the lcm of 329 and 218 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 218 and 329?
The below solved example with step by step work shows how to find what is the lcm of 218 and 329 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 218 and 329?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 218
B = 329
What to be found:
find the lcm of 218 and 329
step 2 Find the prime factors of 218 and 329:
Prime factors of 218 = 2 x 109
Prime factors of 329 = 7 x 47
step 3Identify the repeated and non-repeated prime factors of 218 and 329:
Since there is no common factors between 218 and 329, multiplying the given numbers directly provides the LCM of
218 and 329.
= 218 x 329
= 71722
lcm(218 and 329) = 71722
Hence,
lcm of 218 and 329 is 71722
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 218 and 329.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 218 and 329
What to be found:
lcm (218, 329) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
218 and 329
step 3 Choose the divisor which divides each or most of the given integers (218 and 329), 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 218 and 329 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 218 | 329 |
| 7 | 109 | 329 |
| 47 | 109 | 47 |
| 109 | 109 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 218 and 329:
= 2 x 7 x 47 x 109
= 71722
LCM(218, 329) = 71722
The LCM of two numbers 218 and 329 is 71722