LCM of 36, 48 and 64 is equal to 576. The comprehensive work provides more insight of how to find what is the lcm of 36, 48 and 64 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, 48 and 64?
lcm (36 48 64) = (?)
36 => 2 x 2 x 3 x 3
48 => 2 x 2 x 2 x 2 x 3
64 => 2 x 2 x 2 x 2 x 2 x 2
= 2 x 2 x 2 x 2 x 3 x 3 x 2 x 2
= 576
lcm (36, 48 and 64) = 576
576 is the lcm of 36, 48 and 64.
where,
36 is a positive integer,
48 is a positive integer,
576 is the lcm of 36, 48 and 64,
{2, 2, 2, 2, 3} in {2 x 2 x 3 x 3, 2 x 2 x 2 x 2 x 3, 2 x 2 x 2 x 2 x 2 x 2} are the most repeated factors of 36, 48 and 64,
{3, 2, 2} in {2 x 2 x 3 x 3, 2 x 2 x 2 x 2 x 3, 2 x 2 x 2 x 2 x 2 x 2} are the the other remaining factors of 36, 48 and 64.
Use in Mathematics: LCM of 36, 48 and 64
The below are some of the mathematical applications where lcm of 36, 48 and 64 can be used:
The below solved example with step by step work shows how to find what is the lcm of 36, 48 and 64 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 36, 48 and 64?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 36
B = 48
C = 64
What to be found:
find the lcm of 36, 48 and 64
step 2 Find the prime factors of 36, 48 and 64:
Prime factors of 36 = 2 x 2 x 3 x 3
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
step 3 Identify the repeated and non-repeated prime factors of 36, 48 and 64:
{2, 2, 2, 2, 3} are the most repeated factors and {3, 2, 2} are the non-repeated factors of 36, 48 and 64.
step 4 Find the product of repeated and non-repeated prime factors of 36, 48 and 64:
= 2 x 2 x 2 x 2 x 3 x 3 x 2 x 2
= 576
lcm(20 and 30) = 576
Hence,
lcm of 36, 48 and 64 is 576
2 | 36 | 48 | 64 |
2 | 18 | 24 | 32 |
2 | 9 | 12 | 16 |
2 | 9 | 6 | 8 |
2 | 9 | 3 | 4 |
2 | 9 | 3 | 2 |
3 | 9 | 3 | 1 |
3 | 3 | 1 | 1 |
1 | 1 | 1 |