LCM of 42, 56 and 70 is equal to 840. The comprehensive work provides more insight of how to find what is the lcm of 42, 56 and 70 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 42, 56 and 70?
lcm (42 56 70) = (?)
42 => 2 x 3 x 7
56 => 2 x 2 x 2 x 7
70 => 2 x 5 x 7
= 2 x 7 x 3 x 2 x 2 x 5
= 840
lcm (42, 56 and 70) = 840
840 is the lcm of 42, 56 and 70.
where,
42 is a positive integer,
56 is a positive integer,
840 is the lcm of 42, 56 and 70,
{2, 7} in {2 x 3 x 7, 2 x 2 x 2 x 7, 2 x 5 x 7} are the most repeated factors of 42, 56 and 70,
{3, 2, 2, 5} in {2 x 3 x 7, 2 x 2 x 2 x 7, 2 x 5 x 7} are the the other remaining factors of 42, 56 and 70.
Use in Mathematics: LCM of 42, 56 and 70
The below are some of the mathematical applications where lcm of 42, 56 and 70 can be used:
The below solved example with step by step work shows how to find what is the lcm of 42, 56 and 70 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 42, 56 and 70?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 42
B = 56
C = 70
What to be found:
find the lcm of 42, 56 and 70
step 2 Find the prime factors of 42, 56 and 70:
Prime factors of 42 = 2 x 3 x 7
Prime factors of 56 = 2 x 2 x 2 x 7
Prime factors of 70 = 2 x 5 x 7
step 3 Identify the repeated and non-repeated prime factors of 42, 56 and 70:
{2, 7} are the most repeated factors and {3, 2, 2, 5} are the non-repeated factors of 42, 56 and 70.
step 4 Find the product of repeated and non-repeated prime factors of 42, 56 and 70:
= 2 x 7 x 3 x 2 x 2 x 5
= 840
lcm(20 and 30) = 840
Hence,
lcm of 42, 56 and 70 is 840
2 | 42 | 56 | 70 |
2 | 21 | 28 | 35 |
2 | 21 | 14 | 35 |
3 | 21 | 7 | 35 |
5 | 7 | 7 | 35 |
7 | 7 | 7 | 7 |
1 | 1 | 1 |