LCM of 48 and 328
1968 is the LCM of 48 and 328. 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 48 and 328, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 48 and 328?
lcm (48 328) = (?)
48 => 2 x 2 x 2 x 2 x 3
328 => 2 x 2 x 2 x 41
= 2 x 2 x 2 x 2 x 3 x 41
= 1968
lcm (48 and 328) = 1968
1968 is the LCM of 48 and 328.
where,
48 is a positive integer,
328 is a positive integer,
1968 is the LCM of 48 and 328,
{2 x 2 x 2} in {2 x 2 x 2 x 2 x 3, 2 x 2 x 2 x 41} are the common factors of 48 and 328,
{2 x 3 x 41} in {2 x 2 x 2 x 2 x 3, 2 x 2 x 2 x 41} are the uncommon factors of 48 and 328.
Use in Mathematics: LCM of 48 and 328
The below are some of the mathematical applications where lcm of 48 and 328 can be used:
- to find the least number which is exactly divisible by 48 and 328.
- to find the common denominator for two fractions having 48 and 328 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 48 and 328 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 48 seconds and bell B tolls at 328 seconds repeatedly. The answer is that all bells A and B toll together at 1968 seconds for the first time, at 3936 seconds for the second time, at 5904 seconds for the third time and so on.
Important Notes: 48 and 328 lcm
The below are the important notes to be remembered while solving the lcm of 48 and 328:
- The common prime factors and the remaining prime factors of 48 and 328 should be multiplied to find the least common multiple of 48 and 328, when solving lcm by using prime factors method.
- The results of lcm of 48 and 328, and the lcm of 328 and 48 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 48 and 328?
The below solved example with step by step work shows how to find what is the lcm of 48 and 328 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 48 and 328?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 48
B = 328
What to be found:
find the lcm of 48 and 328
step 2 Find the prime factors of 48 and 328:
Prime factors of 48 = 2 x 2 x 2 x 2 x 3
Prime factors of 328 = 2 x 2 x 2 x 41
step 3 Identify the repeated and non-repeated prime factors of 48 and 328:
{2, 2, 2} are the most repeated factors and {2 x 3 x 41} are the non-repeated factors of 48 and 328.
step 4 Find the product of repeated and non-repeated prime factors of 48 and 328:
= 2 x 2 x 2 x 2 x 3 x 41
= 1968
lcm(48 and 328) = 1968
Hence,
lcm of 48 and 328 is 1968
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 48 and 328.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 48 and 328
What to be found:
lcm (48, 328) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
48 and 328
step 3 Choose the divisor which divides each or most of the given integers (48 and 328), 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 48 and 328 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 48 | 328 |
| 2 | 24 | 164 |
| 2 | 12 | 82 |
| 2 | 6 | 41 |
| 3 | 3 | 41 |
| 41 | 1 | 41 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 48 and 328:
= 2 x 2 x 2 x 2 x 3 x 41
= 1968
LCM(48, 328) = 1968
The LCM of two numbers 48 and 328 is 1968