48, 64 and 88 LCM
LCM of 48, 64 and 88 is equal to 2112. The comprehensive work provides more insight of how to find what is the lcm of 48, 64 and 88 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 48, 64 and 88?
lcm (48 64 88) = (?)
48 => 2 x 2 x 2 x 2 x 3
64 => 2 x 2 x 2 x 2 x 2 x 2
88 => 2 x 2 x 2 x 11
= 2 x 2 x 2 x 2 x 3 x 2 x 2 x 11
= 2112
lcm (48, 64 and 88) = 2112
2112 is the lcm of 48, 64 and 88.
where,
48 is a positive integer,
64 is a positive integer,
2112 is the lcm of 48, 64 and 88,
{2, 2, 2, 2} in {2 x 2 x 2 x 2 x 3, 2 x 2 x 2 x 2 x 2 x 2, 2 x 2 x 2 x 11} are the most repeated factors of 48, 64 and 88,
{3, 2, 2, 11} in {2 x 2 x 2 x 2 x 3, 2 x 2 x 2 x 2 x 2 x 2, 2 x 2 x 2 x 11} are the the other remaining factors of 48, 64 and 88.
Use in Mathematics: LCM of 48, 64 and 88
The below are some of the mathematical applications where lcm of 48, 64 and 88 can be used:
- to find the least number which is exactly divisible by 48, 64 and 88.
- to find the common denominators for the fractions having 48, 64 and 88 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 48, 64 and 88 helps to find the exact time when three similar and recurring 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 all the bells A, B and C toll together, if bell A tolls at 48 seconds, B tolls at 64 seconds and C tolls at 88 seconds repeatedly. The answer is that all bells A, B and C toll together at 2112 seconds for the first time, at 4224 seconds for the second time, at 6336 seconds for the third time and so on.
Important Notes: 48, 64 and 88 lcm
The below are the important notes to be remembered while solving the lcm of 48, 64 and 88:
- The repeated and non-repeated prime factors of 48, 64 and 88 should be multiplied to find the least common multiple of 48, 64 and 88, when solving lcm by using prime factors method.
- The results of lcm of 48, 64 and 88 is identical even if we change the order of given numbers in the lcm calculation, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is the LCM of 48, 64 and 88?
Solved example using prime factors method:
What is the LCM of 48, 64 and 88?
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 48
B = 64
C = 88
What to be found:
find the lcm of 48, 64 and 88
step 2 Find the prime factors of 48, 64 and 88:
Prime factors of 48 = 2 x 2 x 2 x 2 x 3
Prime factors of 64 = 2 x 2 x 2 x 2 x 2 x 2
Prime factors of 88 = 2 x 2 x 2 x 11
step 3 Identify the repeated and non-repeated prime factors of 48, 64 and 88:
{2, 2, 2, 2} are the most repeated factors and {3, 2, 2, 11} are the non-repeated factors of 48, 64 and 88.
step 4 Find the product of repeated and non-repeated prime factors of 48, 64 and 88:
= 2 x 2 x 2 x 2 x 3 x 2 x 2 x 11
= 2112
lcm(20 and 30) = 2112
Hence,
lcm of 48, 64 and 88 is 2112
This special division method is the easiest way to understand the entire calculation of what is the lcm of 48, 64 and 88.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 48, 64 and 88
What to be found:
lcm (48, 64, 88) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
48, 64 and 88
step 3 Choose the divisor which divides each or most of the given integers (48, 64 and 88), 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, 64 and 88 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 48 | 64 | 88 |
| 2 | 24 | 32 | 44 |
| 2 | 12 | 16 | 22 |
| 2 | 6 | 8 | 11 |
| 2 | 3 | 4 | 11 |
| 2 | 3 | 2 | 11 |
| 3 | 3 | 1 | 11 |
| 11 | 1 | 1 | 11 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 48, 64 and 88:
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 11
= 2112
LCM(48, 64, 88) = 2112
The least common multiple for three numbers 48, 64 and 88 is 2112