28 and 96 LCM
LCM of 28 and 96 is equal to 672. The comprehensive work provides more insight of how to find what is the lcm of 28 and 96 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 28 and 96?
lcm (28 96) = (?)
28 => 2 x 2 x 7
96 => 2 x 2 x 2 x 2 x 2 x 3
= 2 x 2 x 7 x 2 x 2 x 2 x 3
= 672
lcm (28 and 96) = 672
672 is the lcm of 28 and 96.
where,
28 is a positive integer,
96 is a positive integer,
672 is the lcm of 28 and 96,
{2 x 2} in {2 x 2 x 7, 2 x 2 x 2 x 2 x 2 x 3} are the common factors of 28 and 96,
{7 x 2 x 2 x 2 x 3} in {2 x 2 x 7, 2 x 2 x 2 x 2 x 2 x 3} are the uncommon factors of 28 and 96.
Use in Mathematics: LCM of 28 and 96
The below are some of the mathematical applications where lcm of 28 and 96 can be used:
- to find the least number which is exactly divisible by 28 and 96.
- to find the common denominator for two fractions having 28 and 96 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 28 and 96 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 28 seconds and bell B tolls at 96 seconds repeatedly. The answer is that all bells A and B toll together at 672 seconds for the first time, at 1344 seconds for the second time, at 2016 seconds for the third time and so on.
Important Notes: 28 and 96 lcm
The below are the important notes to be remembered while solving the lcm of 28 and 96:
- The common prime factors and the remaining prime factors of 28 and 96 should be multiplied to find the least common multiple of 28 and 96, when solving lcm by using prime factors method.
- The results of lcm of 28 and 96, and the lcm of 96 and 28 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 28 and 96?
The below solved example with step by step work shows how to find what is the lcm of 28 and 96 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 28 and 96?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 28
B = 96
What to be found:
find the lcm of 28 and 96
step 2 Find the prime factors of 28 and 96:
Prime factors of 28 = 2 x 2 x 7
Prime factors of 96 = 2 x 2 x 2 x 2 x 2 x 3
step 3 Identify the repeated and non-repeated prime factors of 28 and 96:
{2, 2} are the most repeated factors and {7 x 2 x 2 x 2 x 3} are the non-repeated factors of 28 and 96.
step 4 Find the product of repeated and non-repeated prime factors of 28 and 96:
= 2 x 2 x 7 x 2 x 2 x 2 x 3
= 672
lcm(28 and 96) = 672
Hence,
lcm of 28 and 96 is 672
This special division method is the easiest way to understand the entire calculation of what is the lcm of 28 and 96.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 28 and 96
What to be found:
lcm (28, 96) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
28 and 96
step 3 Choose the divisor which divides each or most of the given integers (28 and 96), 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 28 and 96 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 28 | 96 |
| 2 | 14 | 48 |
| 2 | 7 | 24 |
| 2 | 7 | 12 |
| 2 | 7 | 6 |
| 3 | 7 | 3 |
| 7 | 7 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 28 and 96:
= 2 x 2 x 2 x 2 x 2 x 3 x 7
= 672
LCM(28, 96) = 672
The least common multiple for two numbers 28 and 96 is 672