32 and 34 LCM
LCM of 32 and 34 is equal to 544. The comprehensive work provides more insight of how to find what is the lcm of 32 and 34 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 32 and 34?
lcm (32 34) = (?)
32 => 2 x 2 x 2 x 2 x 2
34 => 2 x 17
= 2 x 2 x 2 x 2 x 2 x 17
= 544
lcm (32 and 34) = 544
544 is the lcm of 32 and 34.
where,
32 is a positive integer,
34 is a positive integer,
544 is the lcm of 32 and 34,
{2} in {2 x 2 x 2 x 2 x 2, 2 x 17} is the common factors of 32 and 34,
{2 x 2 x 2 x 2 x 17} in {2 x 2 x 2 x 2 x 2, 2 x 17} are the uncommon factors of 32 and 34.
Use in Mathematics: LCM of 32 and 34
The below are some of the mathematical applications where lcm of 32 and 34 can be used:
- to find the least number which is exactly divisible by 32 and 34.
- to find the common denominator for two fractions having 32 and 34 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 32 and 34 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 32 seconds and bell B tolls at 34 seconds repeatedly. The answer is that all bells A and B toll together at 544 seconds for the first time, at 1088 seconds for the second time, at 1632 seconds for the third time and so on.
Important Notes: 32 and 34 lcm
The below are the important notes to be remembered while solving the lcm of 32 and 34:
- The common prime factors and the remaining prime factors of 32 and 34 should be multiplied to find the least common multiple of 32 and 34, when solving lcm by using prime factors method.
- The results of lcm of 32 and 34, and the lcm of 34 and 32 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 32 and 34?
The below solved example with step by step work shows how to find what is the lcm of 32 and 34 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 32 and 34?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 32
B = 34
What to be found:
find the lcm of 32 and 34
step 2 Find the prime factors of 32 and 34:
Prime factors of 32 = 2 x 2 x 2 x 2 x 2
Prime factors of 34 = 2 x 17
step 3 Identify the repeated and non-repeated prime factors of 32 and 34:
{2} is the most repeated factor and {2 x 2 x 2 x 2 x 17} are the non-repeated factors of 32 and 34.
step 4 Find the product of repeated and non-repeated prime factors of 32 and 34:
= 2 x 2 x 2 x 2 x 2 x 17
= 544
lcm(32 and 34) = 544
Hence,
lcm of 32 and 34 is 544
This special division method is the easiest way to understand the entire calculation of what is the lcm of 32 and 34.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 32 and 34
What to be found:
lcm (32, 34) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
32 and 34
step 3 Choose the divisor which divides each or most of the given integers (32 and 34), 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 32 and 34 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 32 | 34 |
| 2 | 16 | 17 |
| 2 | 8 | 17 |
| 2 | 4 | 17 |
| 2 | 2 | 17 |
| 17 | 1 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 32 and 34:
= 2 x 2 x 2 x 2 x 2 x 17
= 544
LCM(32, 34) = 544
The least common multiple for two numbers 32 and 34 is 544