LCM of 54, 60 and 90 is equal to 540. The comprehensive work provides more insight of how to find what is the lcm of 54, 60 and 90 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 54, 60 and 90?
lcm (54 60 90) = (?)
54 => 2 x 3 x 3 x 3
60 => 2 x 2 x 3 x 5
90 => 2 x 3 x 3 x 5
= 2 x 3 x 3 x 5 x 3 x 2
= 540
lcm (54, 60 and 90) = 540
540 is the lcm of 54, 60 and 90.
where,
54 is a positive integer,
60 is a positive integer,
540 is the lcm of 54, 60 and 90,
{2, 3, 3, 5} in {2 x 3 x 3 x 3, 2 x 2 x 3 x 5, 2 x 3 x 3 x 5} are the most repeated factors of 54, 60 and 90,
{3, 2} in {2 x 3 x 3 x 3, 2 x 2 x 3 x 5, 2 x 3 x 3 x 5} are the the other remaining factors of 54, 60 and 90.
Use in Mathematics: LCM of 54, 60 and 90
The below are some of the mathematical applications where lcm of 54, 60 and 90 can be used:
The below solved example with step by step work shows how to find what is the lcm of 54, 60 and 90 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 54, 60 and 90?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 54
B = 60
C = 90
What to be found:
find the lcm of 54, 60 and 90
step 2 Find the prime factors of 54, 60 and 90:
Prime factors of 54 = 2 x 3 x 3 x 3
Prime factors of 60 = 2 x 2 x 3 x 5
Prime factors of 90 = 2 x 3 x 3 x 5
step 3 Identify the repeated and non-repeated prime factors of 54, 60 and 90:
{2, 3, 3, 5} are the most repeated factors and {3, 2} are the non-repeated factors of 54, 60 and 90.
step 4 Find the product of repeated and non-repeated prime factors of 54, 60 and 90:
= 2 x 3 x 3 x 5 x 3 x 2
= 540
lcm(20 and 30) = 540
Hence,
lcm of 54, 60 and 90 is 540
2 | 54 | 60 | 90 |
2 | 27 | 30 | 45 |
3 | 27 | 15 | 45 |
3 | 9 | 5 | 15 |
3 | 3 | 5 | 5 |
5 | 1 | 5 | 5 |
1 | 1 | 1 |