LCM of 108 and 144 is equal to 432. The comprehensive work provides more insight of how to find what is the lcm of 108 and 144 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 108 and 144?
lcm (108 144) = (?)
108 => 2 x 2 x 3 x 3 x 3
144 => 2 x 2 x 2 x 2 x 3 x 3
= 2 x 2 x 3 x 3 x 3 x 2 x 2
= 432
lcm (108 and 144) = 432
432 is the lcm of 108 and 144.
where,
108 is a positive integer,
144 is a positive integer,
432 is the lcm of 108 and 144,
{2 x 2 x 3 x 3} in {2 x 2 x 3 x 3 x 3, 2 x 2 x 2 x 2 x 3 x 3} are the common factors of 108 and 144,
{3 x 2 x 2} in {2 x 2 x 3 x 3 x 3, 2 x 2 x 2 x 2 x 3 x 3} are the uncommon factors of 108 and 144.
Use in Mathematics: LCM of 108 and 144
The below are some of the mathematical applications where lcm of 108 and 144 can be used:
The below solved example with step by step work shows how to find what is the lcm of 108 and 144 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 108 and 144?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 108
B = 144
What to be found:
find the lcm of 108 and 144
step 2 Find the prime factors of 108 and 144:
Prime factors of 108 = 2 x 2 x 3 x 3 x 3
Prime factors of 144 = 2 x 2 x 2 x 2 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 108 and 144:
{2, 2, 3, 3} are the most repeated factors and {3 x 2 x 2} are the non-repeated factors of 108 and 144.
step 4 Find the product of repeated and non-repeated prime factors of 108 and 144:
= 2 x 2 x 3 x 3 x 3 x 2 x 2
= 432
lcm(108 and 144) = 432
Hence,
lcm of 108 and 144 is 432
2 | 108 | 144 |
2 | 54 | 72 |
2 | 27 | 36 |
2 | 27 | 18 |
3 | 27 | 9 |
3 | 9 | 3 |
3 | 3 | 1 |
1 | 1 |