LCM of 30, 42 and 54
1890 is the LCM of 30, 42 and 54. 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 30, 42 and 54, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 30, 42 and 54?
lcm (30 42 54) = (?)
30 => 2 x 3 x 5
42 => 2 x 3 x 7
54 => 2 x 3 x 3 x 3
= 2 x 3 x 5 x 7 x 3 x 3
= 1890
lcm (30, 42 and 54) = 1890
The LCM of 30, 42 and 54 is 1890
where,
30 is a positive integer,
42 is a positive integer,
1890 is the LCM of 30, 42 and 54,
{2, 3} in {2 x 3 x 5, 2 x 3 x 7, 2 x 3 x 3 x 3} are the most repeated factors of 30, 42 and 54,
{5, 7, 3, 3} in {2 x 3 x 5, 2 x 3 x 7, 2 x 3 x 3 x 3} are the the other remaining factors of 30, 42 and 54.
Use in Mathematics: LCM of 30, 42 and 54
The below are some of the mathematical applications where lcm of 30, 42 and 54 can be used:
- to find the least number which is exactly divisible by 30, 42 and 54.
- to find the common denominators for the fractions having 30, 42 and 54 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 30, 42 and 54 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 42 seconds and C tolls at 54 seconds repeatedly. The answer is that all bells A, B and C toll together at 1890 seconds for the first time, at 3780 seconds for the second time, at 5670 seconds for the third time and so on.
Important Notes: 30, 42 and 54 lcm
The below are the important notes to be remembered while solving the lcm of 30, 42 and 54:
- The repeated and non-repeated prime factors of 30, 42 and 54 should be multiplied to find the least common multiple of 30, 42 and 54, when solving lcm by using prime factors method.
- The results of lcm of 30, 42 and 54 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 LCM of 30, 42 and 54?
The below solved example with step by step work shows how to find what is the lcm of 30, 42 and 54 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 30, 42 and 54?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 30
B = 42
C = 54
What to be found:
Find lcm of 30, 42 and 54
step 2 Find the prime factors of 30, 42 and 54:
Prime factors of 30 = 2 x 3 x 5
Prime factors of 42 = 2 x 3 x 7
Prime factors of 54 = 2 x 3 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 30, 42 and 54:
{2, 3} are the most repeated factors and {5, 7, 3, 3} are the non-repeated factors of 30, 42 and 54.
step 4 Find the product of repeated and non-repeated prime factors of 30, 42 and 54:
= 2 x 3 x 5 x 7 x 3 x 3
= 1890
LCM(30, 42 and 54) = 1890
Hence,
The Least Common Multiple of 30, 42 and 54 is 1890
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 30, 42 and 54.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 30, 42 and 54
What to be found:
lcm (30, 42, 54) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
30, 42 and 54
step 3 Choose the divisor which divides each or most of the given integers (30, 42 and 54), 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, 42 and 54 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 30 | 42 | 54 |
| 3 | 15 | 21 | 27 |
| 3 | 5 | 7 | 9 |
| 3 | 5 | 7 | 3 |
| 5 | 5 | 7 | 1 |
| 7 | 1 | 7 | 1 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 30, 42 and 54:
= 2 x 3 x 3 x 3 x 5 x 7
= 1890
LCM(30, 42, 54) = 1890
The LCM of three numbers 30, 42 and 54 is 1890