LCM of 72 and 120 is equal to 360. The comprehensive work provides more insight of how to find what is the lcm of 72 and 120 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 72 and 120?
lcm (72 120) = (?)
72 => 2 x 2 x 2 x 3 x 3
120 => 2 x 2 x 2 x 3 x 5
= 2 x 2 x 2 x 3 x 3 x 5
= 360
lcm (72 and 120) = 360
360 is the lcm of 72 and 120.
where,
72 is a positive integer,
120 is a positive integer,
360 is the lcm of 72 and 120,
{2 x 2 x 2 x 3} in {2 x 2 x 2 x 3 x 3, 2 x 2 x 2 x 3 x 5} are the common factors of 72 and 120,
{3 x 5} in {2 x 2 x 2 x 3 x 3, 2 x 2 x 2 x 3 x 5} are the uncommon factors of 72 and 120.
Use in Mathematics: LCM of 72 and 120
The below are some of the mathematical applications where lcm of 72 and 120 can be used:
The below solved example with step by step work shows how to find what is the lcm of 72 and 120 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 72 and 120?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 72
B = 120
What to be found:
find the lcm of 72 and 120
step 2 Find the prime factors of 72 and 120:
Prime factors of 72 = 2 x 2 x 2 x 3 x 3
Prime factors of 120 = 2 x 2 x 2 x 3 x 5
step 3 Identify the repeated and non-repeated prime factors of 72 and 120:
{2, 2, 2, 3} are the most repeated factors and {3 x 5} are the non-repeated factors of 72 and 120.
step 4 Find the product of repeated and non-repeated prime factors of 72 and 120:
= 2 x 2 x 2 x 3 x 3 x 5
= 360
lcm(72 and 120) = 360
Hence,
lcm of 72 and 120 is 360
2 | 72 | 120 |
2 | 36 | 60 |
2 | 18 | 30 |
3 | 9 | 15 |
3 | 3 | 5 |
5 | 1 | 5 |
1 | 1 |