30, 32 and 38 LCM
LCM of 30, 32 and 38 is equal to 9120. The comprehensive work provides more insight of how to find what is the lcm of 30, 32 and 38 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 30, 32 and 38?
lcm (30 32 38) = (?)
30 => 2 x 3 x 5
32 => 2 x 2 x 2 x 2 x 2
38 => 2 x 19
= 2 x 3 x 5 x 2 x 2 x 2 x 2 x 19
= 9120
lcm (30, 32 and 38) = 9120
9120 is the lcm of 30, 32 and 38.
where,
30 is a positive integer,
32 is a positive integer,
9120 is the lcm of 30, 32 and 38,
{2} in {2 x 3 x 5, 2 x 2 x 2 x 2 x 2, 2 x 19} is the most repeated factors of 30, 32 and 38,
{3, 5, 2, 2, 2, 2, 19} in {2 x 3 x 5, 2 x 2 x 2 x 2 x 2, 2 x 19} are the the other remaining factors of 30, 32 and 38.
Use in Mathematics: LCM of 30, 32 and 38
The below are some of the mathematical applications where lcm of 30, 32 and 38 can be used:
- to find the least number which is exactly divisible by 30, 32 and 38.
- to find the common denominators for the fractions having 30, 32 and 38 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 30, 32 and 38 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 30 seconds, B tolls at 32 seconds and C tolls at 38 seconds repeatedly. The answer is that all bells A, B and C toll together at 9120 seconds for the first time, at 18240 seconds for the second time, at 27360 seconds for the third time and so on.
Important Notes: 30, 32 and 38 lcm
The below are the important notes to be remembered while solving the lcm of 30, 32 and 38:
- The repeated and non-repeated prime factors of 30, 32 and 38 should be multiplied to find the least common multiple of 30, 32 and 38, when solving lcm by using prime factors method.
- The results of lcm of 30, 32 and 38 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 30, 32 and 38?
The below solved example with step by step work shows how to find what is the lcm of 30, 32 and 38 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 30, 32 and 38?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 30
B = 32
C = 38
What to be found:
find the lcm of 30, 32 and 38
step 2 Find the prime factors of 30, 32 and 38:
Prime factors of 30 = 2 x 3 x 5
Prime factors of 32 = 2 x 2 x 2 x 2 x 2
Prime factors of 38 = 2 x 19
step 3 Identify the repeated and non-repeated prime factors of 30, 32 and 38:
{2} is the most repeated factor and {3, 5, 2, 2, 2, 2, 19} are the non-repeated factors of 30, 32 and 38.
step 4 Find the product of repeated and non-repeated prime factors of 30, 32 and 38:
= 2 x 3 x 5 x 2 x 2 x 2 x 2 x 19
= 9120
lcm(20 and 30) = 9120
Hence,
lcm of 30, 32 and 38 is 9120
This special division method is the easiest way to understand the entire calculation of what is the lcm of 30, 32 and 38.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 30, 32 and 38
What to be found:
lcm (30, 32, 38) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
30, 32 and 38
step 3 Choose the divisor which divides each or most of the given integers (30, 32 and 38), 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 30, 32 and 38 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 30 | 32 | 38 |
| 2 | 15 | 16 | 19 |
| 2 | 15 | 8 | 19 |
| 2 | 15 | 4 | 19 |
| 2 | 15 | 2 | 19 |
| 3 | 15 | 1 | 19 |
| 5 | 5 | 1 | 19 |
| 19 | 1 | 1 | 19 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 30, 32 and 38:
= 2 x 2 x 2 x 2 x 2 x 3 x 5 x 19
= 9120
LCM(30, 32, 38) = 9120
The least common multiple for three numbers 30, 32 and 38 is 9120