LCM of 21, 28 and 32 is equal to 672. The comprehensive work provides more insight of how to find what is the lcm of 21, 28 and 32 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 21, 28 and 32?
lcm (21 28 32) = (?)
21 => 3 x 7
28 => 2 x 2 x 7
32 => 2 x 2 x 2 x 2 x 2
= 2 x 2 x 7 x 3 x 2 x 2 x 2
= 672
lcm (21, 28 and 32) = 672
672 is the lcm of 21, 28 and 32.
where,
21 is a positive integer,
28 is a positive integer,
672 is the lcm of 21, 28 and 32,
{2, 2, 7} in {3 x 7, 2 x 2 x 7, 2 x 2 x 2 x 2 x 2} are the most repeated factors of 21, 28 and 32,
{3, 2, 2, 2} in {3 x 7, 2 x 2 x 7, 2 x 2 x 2 x 2 x 2} are the the other remaining factors of 21, 28 and 32.
Use in Mathematics: LCM of 21, 28 and 32
The below are some of the mathematical applications where lcm of 21, 28 and 32 can be used:
The below solved example with step by step work shows how to find what is the lcm of 21, 28 and 32 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 21, 28 and 32?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 21
B = 28
C = 32
What to be found:
find the lcm of 21, 28 and 32
step 2 Find the prime factors of 21, 28 and 32:
Prime factors of 21 = 3 x 7
Prime factors of 28 = 2 x 2 x 7
Prime factors of 32 = 2 x 2 x 2 x 2 x 2
step 3 Identify the repeated and non-repeated prime factors of 21, 28 and 32:
{2, 2, 7} are the most repeated factors and {3, 2, 2, 2} are the non-repeated factors of 21, 28 and 32.
step 4 Find the product of repeated and non-repeated prime factors of 21, 28 and 32:
= 2 x 2 x 7 x 3 x 2 x 2 x 2
= 672
lcm(20 and 30) = 672
Hence,
lcm of 21, 28 and 32 is 672
2 | 21 | 28 | 32 |
2 | 21 | 14 | 16 |
2 | 21 | 7 | 8 |
2 | 21 | 7 | 4 |
2 | 21 | 7 | 2 |
3 | 21 | 7 | 1 |
7 | 7 | 7 | 1 |
1 | 1 | 1 |