LCM of 20, 42 and 76 is equal to 7980. The comprehensive work provides more insight of how to find what is the lcm of 20, 42 and 76 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 20, 42 and 76?
lcm (20 42 76) = (?)
20 => 2 x 2 x 5
42 => 2 x 3 x 7
76 => 2 x 2 x 19
= 2 x 2 x 5 x 3 x 7 x 19
= 7980
lcm (20, 42 and 76) = 7980
7980 is the lcm of 20, 42 and 76.
where,
20 is a positive integer,
42 is a positive integer,
7980 is the lcm of 20, 42 and 76,
{2, 2} in {2 x 2 x 5, 2 x 3 x 7, 2 x 2 x 19} are the most repeated factors of 20, 42 and 76,
{5, 3, 7, 19} in {2 x 2 x 5, 2 x 3 x 7, 2 x 2 x 19} are the the other remaining factors of 20, 42 and 76.
Use in Mathematics: LCM of 20, 42 and 76
The below are some of the mathematical applications where lcm of 20, 42 and 76 can be used:
The below solved example with step by step work shows how to find what is the lcm of 20, 42 and 76 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 20, 42 and 76?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 20
B = 42
C = 76
What to be found:
find the lcm of 20, 42 and 76
step 2 Find the prime factors of 20, 42 and 76:
Prime factors of 20 = 2 x 2 x 5
Prime factors of 42 = 2 x 3 x 7
Prime factors of 76 = 2 x 2 x 19
step 3 Identify the repeated and non-repeated prime factors of 20, 42 and 76:
{2, 2} are the most repeated factors and {5, 3, 7, 19} are the non-repeated factors of 20, 42 and 76.
step 4 Find the product of repeated and non-repeated prime factors of 20, 42 and 76:
= 2 x 2 x 5 x 3 x 7 x 19
= 7980
lcm(20 and 30) = 7980
Hence,
lcm of 20, 42 and 76 is 7980
2 | 20 | 42 | 76 |
2 | 10 | 21 | 38 |
3 | 5 | 21 | 19 |
5 | 5 | 7 | 19 |
7 | 1 | 7 | 19 |
19 | 1 | 1 | 19 |
1 | 1 | 1 |