LCM of 45 and 192
2880 is the LCM of 45 and 192. 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 45 and 192, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 45 and 192?
lcm (45 192) = (?)
45 => 3 x 3 x 5
192 => 2 x 2 x 2 x 2 x 2 x 2 x 3
= 3 x 3 x 5 x 2 x 2 x 2 x 2 x 2 x 2
= 2880
lcm (45 and 192) = 2880
2880 is the LCM of 45 and 192.
where,
45 is a positive integer,
192 is a positive integer,
2880 is the LCM of 45 and 192,
{3} in {3 x 3 x 5, 2 x 2 x 2 x 2 x 2 x 2 x 3} is the common factors of 45 and 192,
{3 x 5 x 2 x 2 x 2 x 2 x 2 x 2} in {3 x 3 x 5, 2 x 2 x 2 x 2 x 2 x 2 x 3} are the uncommon factors of 45 and 192.
Use in Mathematics: LCM of 45 and 192
The below are some of the mathematical applications where lcm of 45 and 192 can be used:
- to find the least number which is exactly divisible by 45 and 192.
- to find the common denominator for two fractions having 45 and 192 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 45 and 192 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 45 seconds and bell B tolls at 192 seconds repeatedly. The answer is that all bells A and B toll together at 2880 seconds for the first time, at 5760 seconds for the second time, at 8640 seconds for the third time and so on.
Important Notes: 45 and 192 lcm
The below are the important notes to be remembered while solving the lcm of 45 and 192:
- The common prime factors and the remaining prime factors of 45 and 192 should be multiplied to find the least common multiple of 45 and 192, when solving lcm by using prime factors method.
- The results of lcm of 45 and 192, and the lcm of 192 and 45 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 45 and 192?
The below solved example with step by step work shows how to find what is the lcm of 45 and 192 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 45 and 192?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 45
B = 192
What to be found:
find the lcm of 45 and 192
step 2 Find the prime factors of 45 and 192:
Prime factors of 45 = 3 x 3 x 5
Prime factors of 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3
step 3 Identify the repeated and non-repeated prime factors of 45 and 192:
{3} is the most repeated factor and {3 x 5 x 2 x 2 x 2 x 2 x 2 x 2} are the non-repeated factors of 45 and 192.
step 4 Find the product of repeated and non-repeated prime factors of 45 and 192:
= 3 x 3 x 5 x 2 x 2 x 2 x 2 x 2 x 2
= 2880
lcm(45 and 192) = 2880
Hence,
lcm of 45 and 192 is 2880
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 45 and 192.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 45 and 192
What to be found:
lcm (45, 192) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
45 and 192
step 3 Choose the divisor which divides each or most of the given integers (45 and 192), 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 45 and 192 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 45 | 192 |
| 2 | 45 | 96 |
| 2 | 45 | 48 |
| 2 | 45 | 24 |
| 2 | 45 | 12 |
| 2 | 45 | 6 |
| 3 | 45 | 3 |
| 3 | 15 | 1 |
| 5 | 5 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 45 and 192:
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5
= 2880
LCM(45, 192) = 2880
The LCM of two numbers 45 and 192 is 2880