LCM of 34 and 221
442 is the LCM of 34 and 221. 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 221, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 34 and 221?
lcm (34 221) = (?)
34 => 2 x 17
221 => 13 x 17
= 17 x 2 x 13
= 442
lcm (34 and 221) = 442
442 is the LCM of 34 and 221.
where,
34 is a positive integer,
221 is a positive integer,
442 is the LCM of 34 and 221,
{17} in {2 x 17, 13 x 17} is the common factors of 34 and 221,
{2 x 13} in {2 x 17, 13 x 17} are the uncommon factors of 34 and 221.
Use in Mathematics: LCM of 34 and 221
The below are some of the mathematical applications where lcm of 34 and 221 can be used:
- to find the least number which is exactly divisible by 34 and 221.
- to find the common denominator for two fractions having 34 and 221 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 34 and 221 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 221 seconds repeatedly. The answer is that all bells A and B toll together at 442 seconds for the first time, at 884 seconds for the second time, at 1326 seconds for the third time and so on.
Important Notes: 34 and 221 lcm
The below are the important notes to be remembered while solving the lcm of 34 and 221:
- The common prime factors and the remaining prime factors of 34 and 221 should be multiplied to find the least common multiple of 34 and 221, when solving lcm by using prime factors method.
- The results of lcm of 34 and 221, and the lcm of 221 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 221?
The below solved example with step by step work shows how to find what is the lcm of 34 and 221 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 34 and 221?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 34
B = 221
What to be found:
find the lcm of 34 and 221
step 2 Find the prime factors of 34 and 221:
Prime factors of 34 = 2 x 17
Prime factors of 221 = 13 x 17
step 3 Identify the repeated and non-repeated prime factors of 34 and 221:
{17} is the most repeated factor and {2 x 13} are the non-repeated factors of 34 and 221.
step 4 Find the product of repeated and non-repeated prime factors of 34 and 221:
= 17 x 2 x 13
= 442
lcm(34 and 221) = 442
Hence,
lcm of 34 and 221 is 442
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 34 and 221.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 34 and 221
What to be found:
lcm (34, 221) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
34 and 221
step 3 Choose the divisor which divides each or most of the given integers (34 and 221), 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 221 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 34 | 221 |
| 13 | 17 | 221 |
| 17 | 17 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 34 and 221:
= 2 x 13 x 17
= 442
LCM(34, 221) = 442
The LCM of two numbers 34 and 221 is 442