Question #8a3cc

2 Answers
Apr 10, 2017

120

Explanation:

color(white)(.....)8color(white)(123456789)12color(white)(123456789)15
...............color(white)(129)............color(white)(1298).............
color(white)(.....)8color(white)(..............)12color(white)(................)15
color(white)(.....)16color(white)(.............)24color(white)(................)30
color(white)(.....)24color(white)(.............)36color(white)(................)45
color(white)(.....)32color(white)(.............)48color(white)(................)60
color(white)(.....)40color(white)(.............)60color(white)(................)75
color(white)(.....)48color(white)(.............)72color(white)(................)90
color(white)(.....)56color(white)(.............)84color(white)(................)105
color(white)(.....)64color(white)(.............)96color(white)(................)color(green)(120)
color(white)(.....)72color(white)(.............)108color(white)(................)color(white)(30)
color(white)(.....)80color(white)(.............)color(green)(120)color(white)(................)color(white)(30)
color(white)(.....)88color(white)(.............)color(white)(24)color(white)(................)color(white)(30)
color(white)(.....)96color(white)(.............)color(white)(24)color(white)(................)color(white)(30)
color(white)(.....)104color(white)(.............)color(white)(24)color(white)(................)color(white)(30)
color(white)(.....)112color(white)(.............)color(white)(24)color(white)(................)color(white)(30)
color(white)(.....)color(green)(120)color(white)(.............)color(white)(24)color(white)(................)color(white)(30)

The LCM is 120

Apr 10, 2017

120

Explanation:

The easiest way to do this is to find the prime factorization of each number first.

8 = 4 * 2
8 = 2 * 2 * 2
8 = 2^3

12 = 6 * 2
12 = 3 * 2 * 2
12 = 3 * 2^2

15 = 5 * 3

Now that we have reduced all numbers to their prime factorizations, we will look for the factors with the highest exponent and multiply them all together to get our LCM.

There is 2^3 from 8 , 3^1 from 12 and 15 , and 5^1 from 15 .

So now we must do the following:

2^3 * 3 * 5
2 * 2 * 2 * 3 * 5
120

Therefore, the LCM of 8 , 12 , and 15 is 120 .