LCM of 27 and 84 is equal to 756. The comprehensive work provides more insight of how to find what is the lcm of 27 and 84 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 27 and 84?
lcm (27 84) = (?)
27 => 3 x 3 x 3
84 => 2 x 2 x 3 x 7
= 3 x 3 x 3 x 2 x 2 x 7
= 756
lcm (27 and 84) = 756
756 is the lcm of 27 and 84.
where,
27 is a positive integer,
84 is a positive integer,
756 is the lcm of 27 and 84,
{3} in {3 x 3 x 3, 2 x 2 x 3 x 7} is the common factors of 27 and 84,
{3 x 3 x 2 x 2 x 7} in {3 x 3 x 3, 2 x 2 x 3 x 7} are the uncommon factors of 27 and 84.
Use in Mathematics: LCM of 27 and 84
The below are some of the mathematical applications where lcm of 27 and 84 can be used:
The below solved example with step by step work shows how to find what is the lcm of 27 and 84 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 27 and 84?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 27
B = 84
What to be found:
find the lcm of 27 and 84
step 2 Find the prime factors of 27 and 84:
Prime factors of 27 = 3 x 3 x 3
Prime factors of 84 = 2 x 2 x 3 x 7
step 3 Identify the repeated and non-repeated prime factors of 27 and 84:
{3} is the most repeated factor and {3 x 3 x 2 x 2 x 7} are the non-repeated factors of 27 and 84.
step 4 Find the product of repeated and non-repeated prime factors of 27 and 84:
= 3 x 3 x 3 x 2 x 2 x 7
= 756
lcm(27 and 84) = 756
Hence,
lcm of 27 and 84 is 756
2 | 27 | 84 |
2 | 27 | 42 |
3 | 27 | 21 |
3 | 9 | 7 |
3 | 3 | 7 |
7 | 1 | 7 |
1 | 1 |