LCM of 10, 12 and 42 is equal to 420. The comprehensive work provides more insight of how to find what is the lcm of 10, 12 and 42 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 42?
lcm (10 12 42) = (?)
10 => 2 x 5
12 => 2 x 2 x 3
42 => 2 x 3 x 7
= 2 x 3 x 5 x 2 x 7
= 420
lcm (10, 12 and 42) = 420
420 is the lcm of 10, 12 and 42.
where,
10 is a positive integer,
12 is a positive integer,
420 is the lcm of 10, 12 and 42,
{2, 3} in {2 x 5, 2 x 2 x 3, 2 x 3 x 7} are the most repeated factors of 10, 12 and 42,
{5, 2, 7} in {2 x 5, 2 x 2 x 3, 2 x 3 x 7} are the the other remaining factors of 10, 12 and 42.
Use in Mathematics: LCM of 10, 12 and 42
The below are some of the mathematical applications where lcm of 10, 12 and 42 can be used:
The below solved example with step by step work shows how to find what is the lcm of 10, 12 and 42 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 10, 12 and 42?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 10
B = 12
C = 42
What to be found:
find the lcm of 10, 12 and 42
step 2 Find the prime factors of 10, 12 and 42:
Prime factors of 10 = 2 x 5
Prime factors of 12 = 2 x 2 x 3
Prime factors of 42 = 2 x 3 x 7
step 3 Identify the repeated and non-repeated prime factors of 10, 12 and 42:
{2, 3} are the most repeated factors and {5, 2, 7} are the non-repeated factors of 10, 12 and 42.
step 4 Find the product of repeated and non-repeated prime factors of 10, 12 and 42:
= 2 x 3 x 5 x 2 x 7
= 420
lcm(20 and 30) = 420
Hence,
lcm of 10, 12 and 42 is 420
2 | 10 | 12 | 42 |
2 | 5 | 6 | 21 |
3 | 5 | 3 | 21 |
5 | 5 | 1 | 7 |
7 | 1 | 1 | 7 |
1 | 1 | 1 |