LCM of 319 and 351
111969 is the LCM of 319 and 351. 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 319 and 351, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 319 and 351?
lcm (319 351) = (?)
319 => 11 x 29
351 => 3 x 3 x 3 x 13
= 11 x 29 x 3 x 3 x 3 x 13
= 111969
lcm (319 and 351) = 111969
111969 is the LCM of 319 and 351.
where,
319 is a positive integer,
351 is a positive integer,
111969 is the LCM of 319 and 351,
There is no common factors of 319 and 351 in {11 x 29, 3 x 3 x 3 x 13},
{11 x 29 x 3 x 3 x 3 x 13} in {11 x 29, 3 x 3 x 3 x 13} are the uncommon factors of 319 and 351.
Use in Mathematics: LCM of 319 and 351
The below are some of the mathematical applications where lcm of 319 and 351 can be used:
- to find the least number which is exactly divisible by 319 and 351.
- to find the common denominator for two fractions having 319 and 351 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 319 and 351 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 319 seconds and bell B tolls at 351 seconds repeatedly. The answer is that all bells A and B toll together at 111969 seconds for the first time, at 223938 seconds for the second time, at 335907 seconds for the third time and so on.
Important Notes: 319 and 351 lcm
The below are the important notes to be remembered while solving the lcm of 319 and 351:
- The common prime factors and the remaining prime factors of 319 and 351 should be multiplied to find the least common multiple of 319 and 351, when solving lcm by using prime factors method.
- The results of lcm of 319 and 351, and the lcm of 351 and 319 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 319 and 351?
The below solved example with step by step work shows how to find what is the lcm of 319 and 351 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 319 and 351?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 319
B = 351
What to be found:
find the lcm of 319 and 351
step 2 Find the prime factors of 319 and 351:
Prime factors of 319 = 11 x 29
Prime factors of 351 = 3 x 3 x 3 x 13
step 3Identify the repeated and non-repeated prime factors of 319 and 351:
Since there is no common factors between 319 and 351, multiplying the given numbers directly provides the LCM of
319 and 351.
= 319 x 351
= 111969
lcm(319 and 351) = 111969
Hence,
lcm of 319 and 351 is 111969
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 319 and 351.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 319 and 351
What to be found:
lcm (319, 351) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
319 and 351
step 3 Choose the divisor which divides each or most of the given integers (319 and 351), 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 319 and 351 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 319 | 351 |
| 3 | 319 | 117 |
| 3 | 319 | 39 |
| 11 | 319 | 13 |
| 13 | 29 | 13 |
| 29 | 29 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 319 and 351:
= 3 x 3 x 3 x 11 x 13 x 29
= 111969
LCM(319, 351) = 111969
The LCM of two numbers 319 and 351 is 111969