LCM of 32 and 109
3488 is the LCM of 32 and 109. 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 32 and 109, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 32 and 109?
lcm (32 109) = (?)
32 => 2 x 2 x 2 x 2 x 2
109 => 109
= 2 x 2 x 2 x 2 x 2 x 109
= 3488
lcm (32 and 109) = 3488
3488 is the LCM of 32 and 109.
where,
32 is a positive integer,
109 is a positive integer,
3488 is the LCM of 32 and 109,
There is no common factors of 32 and 109 in {2 x 2 x 2 x 2 x 2, 109},
{2 x 2 x 2 x 2 x 2 x 109} in {2 x 2 x 2 x 2 x 2, 109} are the uncommon factors of 32 and 109.
Use in Mathematics: LCM of 32 and 109
The below are some of the mathematical applications where lcm of 32 and 109 can be used:
- to find the least number which is exactly divisible by 32 and 109.
- to find the common denominator for two fractions having 32 and 109 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 32 and 109 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 109 seconds repeatedly. The answer is that all bells A and B toll together at 3488 seconds for the first time, at 6976 seconds for the second time, at 10464 seconds for the third time and so on.
Important Notes: 32 and 109 lcm
The below are the important notes to be remembered while solving the lcm of 32 and 109:
- The common prime factors and the remaining prime factors of 32 and 109 should be multiplied to find the least common multiple of 32 and 109, when solving lcm by using prime factors method.
- The results of lcm of 32 and 109, and the lcm of 109 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 109?
The below solved example with step by step work shows how to find what is the lcm of 32 and 109 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 32 and 109?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 32
B = 109
What to be found:
find the lcm of 32 and 109
step 2 Find the prime factors of 32 and 109:
Prime factors of 32 = 2 x 2 x 2 x 2 x 2
Prime factors of 109 = 109
step 3Identify the repeated and non-repeated prime factors of 32 and 109:
Since there is no common factors between 32 and 109, multiplying the given numbers directly provides the LCM of
32 and 109.
= 32 x 109
= 3488
lcm(32 and 109) = 3488
Hence,
lcm of 32 and 109 is 3488
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 32 and 109.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 32 and 109
What to be found:
lcm (32, 109) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
32 and 109
step 3 Choose the divisor which divides each or most of the given integers (32 and 109), 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 109 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 32 | 109 |
| 2 | 16 | 109 |
| 2 | 8 | 109 |
| 2 | 4 | 109 |
| 2 | 2 | 109 |
| 109 | 1 | 109 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 32 and 109:
= 2 x 2 x 2 x 2 x 2 x 109
= 3488
LCM(32, 109) = 3488
The LCM of two numbers 32 and 109 is 3488