LCM of 14, 18 and 20 is equal to 1260. The comprehensive work provides more insight of how to find what is the lcm of 14, 18 and 20 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 14, 18 and 20?
lcm (14 18 20) = (?)
14 => 2 x 7
18 => 2 x 3 x 3
20 => 2 x 2 x 5
= 2 x 7 x 3 x 3 x 2 x 5
= 1260
lcm (14, 18 and 20) = 1260
1260 is the lcm of 14, 18 and 20.
where,
14 is a positive integer,
18 is a positive integer,
1260 is the lcm of 14, 18 and 20,
{2} in {2 x 7, 2 x 3 x 3, 2 x 2 x 5} is the most repeated factors of 14, 18 and 20,
{7, 3, 3, 2, 5} in {2 x 7, 2 x 3 x 3, 2 x 2 x 5} are the the other remaining factors of 14, 18 and 20.
Use in Mathematics: LCM of 14, 18 and 20
The below are some of the mathematical applications where lcm of 14, 18 and 20 can be used:
The below solved example with step by step work shows how to find what is the lcm of 14, 18 and 20 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 14, 18 and 20?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 14
B = 18
C = 20
What to be found:
find the lcm of 14, 18 and 20
step 2 Find the prime factors of 14, 18 and 20:
Prime factors of 14 = 2 x 7
Prime factors of 18 = 2 x 3 x 3
Prime factors of 20 = 2 x 2 x 5
step 3 Identify the repeated and non-repeated prime factors of 14, 18 and 20:
{2} is the most repeated factor and {7, 3, 3, 2, 5} are the non-repeated factors of 14, 18 and 20.
step 4 Find the product of repeated and non-repeated prime factors of 14, 18 and 20:
= 2 x 7 x 3 x 3 x 2 x 5
= 1260
lcm(20 and 30) = 1260
Hence,
lcm of 14, 18 and 20 is 1260
2 | 14 | 18 | 20 |
2 | 7 | 9 | 10 |
3 | 7 | 9 | 5 |
3 | 7 | 3 | 5 |
5 | 7 | 1 | 5 |
7 | 7 | 1 | 1 |
1 | 1 | 1 |