LCM of 34 and 289
578 is the LCM of 34 and 289. 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 34 and 289, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 34 and 289?
lcm (34 289) = (?)
34 => 2 x 17
289 => 17 x 17
= 17 x 2 x 17
= 578
lcm (34 and 289) = 578
578 is the LCM of 34 and 289.
where,
34 is a positive integer,
289 is a positive integer,
578 is the LCM of 34 and 289,
{17} in {2 x 17, 17 x 17} is the common factors of 34 and 289,
{2 x 17} in {2 x 17, 17 x 17} are the uncommon factors of 34 and 289.
Use in Mathematics: LCM of 34 and 289
The below are some of the mathematical applications where lcm of 34 and 289 can be used:
- to find the least number which is exactly divisible by 34 and 289.
- to find the common denominator for two fractions having 34 and 289 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 34 and 289 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 34 seconds and bell B tolls at 289 seconds repeatedly. The answer is that all bells A and B toll together at 578 seconds for the first time, at 1156 seconds for the second time, at 1734 seconds for the third time and so on.
Important Notes: 34 and 289 lcm
The below are the important notes to be remembered while solving the lcm of 34 and 289:
- The common prime factors and the remaining prime factors of 34 and 289 should be multiplied to find the least common multiple of 34 and 289, when solving lcm by using prime factors method.
- The results of lcm of 34 and 289, and the lcm of 289 and 34 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 34 and 289?
The below solved example with step by step work shows how to find what is the lcm of 34 and 289 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 34 and 289?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 34
B = 289
What to be found:
find the lcm of 34 and 289
step 2 Find the prime factors of 34 and 289:
Prime factors of 34 = 2 x 17
Prime factors of 289 = 17 x 17
step 3 Identify the repeated and non-repeated prime factors of 34 and 289:
{17} is the most repeated factor and {2 x 17} are the non-repeated factors of 34 and 289.
step 4 Find the product of repeated and non-repeated prime factors of 34 and 289:
= 17 x 2 x 17
= 578
lcm(34 and 289) = 578
Hence,
lcm of 34 and 289 is 578
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 34 and 289.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 34 and 289
What to be found:
lcm (34, 289) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
34 and 289
step 3 Choose the divisor which divides each or most of the given integers (34 and 289), 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 34 and 289 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 34 | 289 |
| 17 | 17 | 289 |
| 17 | 1 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 34 and 289:
= 2 x 17 x 17
= 578
LCM(34, 289) = 578
The LCM of two numbers 34 and 289 is 578