36, 54 and 72 LCM
LCM of 36, 54 and 72 is equal to 216. The comprehensive work provides more insight of how to find what is the lcm of 36, 54 and 72 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 36, 54 and 72?
lcm (36 54 72) = (?)
36 => 2 x 2 x 3 x 3
54 => 2 x 3 x 3 x 3
72 => 2 x 2 x 2 x 3 x 3
= 2 x 2 x 3 x 3 x 3 x 2
= 216
lcm (36, 54 and 72) = 216
216 is the lcm of 36, 54 and 72.
where,
36 is a positive integer,
54 is a positive integer,
216 is the lcm of 36, 54 and 72,
{2, 2, 3, 3} in {2 x 2 x 3 x 3, 2 x 3 x 3 x 3, 2 x 2 x 2 x 3 x 3} are the most repeated factors of 36, 54 and 72,
{3, 2} in {2 x 2 x 3 x 3, 2 x 3 x 3 x 3, 2 x 2 x 2 x 3 x 3} are the the other remaining factors of 36, 54 and 72.
Use in Mathematics: LCM of 36, 54 and 72
The below are some of the mathematical applications where lcm of 36, 54 and 72 can be used:
- to find the least number which is exactly divisible by 36, 54 and 72.
- to find the common denominators for the fractions having 36, 54 and 72 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 36, 54 and 72 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 36 seconds, B tolls at 54 seconds and C tolls at 72 seconds repeatedly. The answer is that all bells A, B and C toll together at 216 seconds for the first time, at 432 seconds for the second time, at 648 seconds for the third time and so on.
Important Notes: 36, 54 and 72 lcm
The below are the important notes to be remembered while solving the lcm of 36, 54 and 72:
- The repeated and non-repeated prime factors of 36, 54 and 72 should be multiplied to find the least common multiple of 36, 54 and 72, when solving lcm by using prime factors method.
- The results of lcm of 36, 54 and 72 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 36, 54 and 72?
The below solved example with step by step work shows how to find what is the lcm of 36, 54 and 72 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 36, 54 and 72?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 36
B = 54
C = 72
What to be found:
find the lcm of 36, 54 and 72
step 2 Find the prime factors of 36, 54 and 72:
Prime factors of 36 = 2 x 2 x 3 x 3
Prime factors of 54 = 2 x 3 x 3 x 3
Prime factors of 72 = 2 x 2 x 2 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 36, 54 and 72:
{2, 2, 3, 3} are the most repeated factors and {3, 2} are the non-repeated factors of 36, 54 and 72.
step 4 Find the product of repeated and non-repeated prime factors of 36, 54 and 72:
= 2 x 2 x 3 x 3 x 3 x 2
= 216
lcm(20 and 30) = 216
Hence,
lcm of 36, 54 and 72 is 216
This special division method is the easiest way to understand the entire calculation of what is the lcm of 36, 54 and 72.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 36, 54 and 72
What to be found:
lcm (36, 54, 72) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
36, 54 and 72
step 3 Choose the divisor which divides each or most of the given integers (36, 54 and 72), 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 36, 54 and 72 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 36 | 54 | 72 |
| 2 | 18 | 27 | 36 |
| 2 | 9 | 27 | 18 |
| 3 | 9 | 27 | 9 |
| 3 | 3 | 9 | 3 |
| 3 | 1 | 3 | 1 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 36, 54 and 72:
= 2 x 2 x 2 x 3 x 3 x 3
= 216
LCM(36, 54, 72) = 216
The least common multiple for three numbers 36, 54 and 72 is 216