LCM of 10, 12 and 14 is equal to 420. The comprehensive work provides more insight of how to find what is the lcm of 10, 12 and 14 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 10, 12 and 14?
lcm (10 12 14) = (?)
10 => 2 x 5
12 => 2 x 2 x 3
14 => 2 x 7
= 2 x 5 x 2 x 3 x 7
= 420
lcm (10, 12 and 14) = 420
420 is the lcm of 10, 12 and 14.
where,
10 is a positive integer,
12 is a positive integer,
420 is the lcm of 10, 12 and 14,
{2} in {2 x 5, 2 x 2 x 3, 2 x 7} is the most repeated factors of 10, 12 and 14,
{5, 2, 3, 7} in {2 x 5, 2 x 2 x 3, 2 x 7} are the the other remaining factors of 10, 12 and 14.
Use in Mathematics: LCM of 10, 12 and 14
The below are some of the mathematical applications where lcm of 10, 12 and 14 can be used:
The below solved example with step by step work shows how to find what is the lcm of 10, 12 and 14 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 10, 12 and 14?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 10
B = 12
C = 14
What to be found:
find the lcm of 10, 12 and 14
step 2 Find the prime factors of 10, 12 and 14:
Prime factors of 10 = 2 x 5
Prime factors of 12 = 2 x 2 x 3
Prime factors of 14 = 2 x 7
step 3 Identify the repeated and non-repeated prime factors of 10, 12 and 14:
{2} is the most repeated factor and {5, 2, 3, 7} are the non-repeated factors of 10, 12 and 14.
step 4 Find the product of repeated and non-repeated prime factors of 10, 12 and 14:
= 2 x 5 x 2 x 3 x 7
= 420
lcm(20 and 30) = 420
Hence,
lcm of 10, 12 and 14 is 420
2 | 10 | 12 | 14 |
2 | 5 | 6 | 7 |
3 | 5 | 3 | 7 |
5 | 5 | 1 | 7 |
7 | 1 | 1 | 7 |
1 | 1 | 1 |