34 and 102 LCM
LCM of 34 and 102 is equal to 102. The comprehensive work provides more insight of how to find what is the lcm of 34 and 102 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 34 and 102?
lcm (34 102) = (?)
34 => 2 x 17
102 => 2 x 3 x 17
= 2 x 17 x 3
= 102
lcm (34 and 102) = 102
102 is the lcm of 34 and 102.
where,
34 is a positive integer,
102 is a positive integer,
102 is the lcm of 34 and 102,
{2 x 17} in {2 x 17, 2 x 3 x 17} are the common factors of 34 and 102,
{3} in {2 x 17, 2 x 3 x 17} is the uncommon factors of 34 and 102.
Use in Mathematics: LCM of 34 and 102
The below are some of the mathematical applications where lcm of 34 and 102 can be used:
- to find the least number which is exactly divisible by 34 and 102.
- to find the common denominator for two fractions having 34 and 102 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 34 and 102 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 102 seconds repeatedly. The answer is that all bells A and B toll together at 102 seconds for the first time, at 204 seconds for the second time, at 306 seconds for the third time and so on.
Important Notes: 34 and 102 lcm
The below are the important notes to be remembered while solving the lcm of 34 and 102:
- The common prime factors and the remaining prime factors of 34 and 102 should be multiplied to find the least common multiple of 34 and 102, when solving lcm by using prime factors method.
- The results of lcm of 34 and 102, and the lcm of 102 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 102?
The below solved example with step by step work shows how to find what is the lcm of 34 and 102 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 34 and 102?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 34
B = 102
What to be found:
find the lcm of 34 and 102
step 2 Find the prime factors of 34 and 102:
Prime factors of 34 = 2 x 17
Prime factors of 102 = 2 x 3 x 17
step 3 Identify the repeated and non-repeated prime factors of 34 and 102:
{2, 17} are the most repeated factors and {3} is the non-repeated factor of 34 and 102.
step 4 Find the product of repeated and non-repeated prime factors of 34 and 102:
= 2 x 17 x 3
= 102
lcm(34 and 102) = 102
Hence,
lcm of 34 and 102 is 102
This special division method is the easiest way to understand the entire calculation of what is the lcm of 34 and 102.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 34 and 102
What to be found:
lcm (34, 102) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
34 and 102
step 3 Choose the divisor which divides each or most of the given integers (34 and 102), 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 102 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 34 | 102 |
| 3 | 17 | 51 |
| 17 | 17 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 34 and 102:
= 2 x 3 x 17
= 102
LCM(34, 102) = 102
The least common multiple for two numbers 34 and 102 is 102