LCM of 96 and 125
12000 is the LCM of 96 and 125. 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 96 and 125, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 96 and 125?
lcm (96 125) = (?)
96 => 2 x 2 x 2 x 2 x 2 x 3
125 => 5 x 5 x 5
= 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5
= 12000
lcm (96 and 125) = 12000
12000 is the LCM of 96 and 125.
where,
96 is a positive integer,
125 is a positive integer,
12000 is the LCM of 96 and 125,
There is no common factors of 96 and 125 in {2 x 2 x 2 x 2 x 2 x 3, 5 x 5 x 5},
{2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5} in {2 x 2 x 2 x 2 x 2 x 3, 5 x 5 x 5} are the uncommon factors of 96 and 125.
Use in Mathematics: LCM of 96 and 125
The below are some of the mathematical applications where lcm of 96 and 125 can be used:
- to find the least number which is exactly divisible by 96 and 125.
- to find the common denominator for two fractions having 96 and 125 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 96 and 125 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 96 seconds and bell B tolls at 125 seconds repeatedly. The answer is that all bells A and B toll together at 12000 seconds for the first time, at 24000 seconds for the second time, at 36000 seconds for the third time and so on.
Important Notes: 96 and 125 lcm
The below are the important notes to be remembered while solving the lcm of 96 and 125:
- The common prime factors and the remaining prime factors of 96 and 125 should be multiplied to find the least common multiple of 96 and 125, when solving lcm by using prime factors method.
- The results of lcm of 96 and 125, and the lcm of 125 and 96 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 96 and 125?
The below solved example with step by step work shows how to find what is the lcm of 96 and 125 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 96 and 125?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 96
B = 125
What to be found:
find the lcm of 96 and 125
step 2 Find the prime factors of 96 and 125:
Prime factors of 96 = 2 x 2 x 2 x 2 x 2 x 3
Prime factors of 125 = 5 x 5 x 5
step 3Identify the repeated and non-repeated prime factors of 96 and 125:
Since there is no common factors between 96 and 125, multiplying the given numbers directly provides the LCM of
96 and 125.
= 96 x 125
= 12000
lcm(96 and 125) = 12000
Hence,
lcm of 96 and 125 is 12000
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 96 and 125.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 96 and 125
What to be found:
lcm (96, 125) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
96 and 125
step 3 Choose the divisor which divides each or most of the given integers (96 and 125), 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 96 and 125 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 96 | 125 |
| 2 | 48 | 125 |
| 2 | 24 | 125 |
| 2 | 12 | 125 |
| 2 | 6 | 125 |
| 3 | 3 | 125 |
| 5 | 1 | 125 |
| 5 | 1 | 25 |
| 5 | 1 | 5 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 96 and 125:
= 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5
= 12000
LCM(96, 125) = 12000
The LCM of two numbers 96 and 125 is 12000