Which of the following sets of numbers have the same lcm as 12, 10, 5?

a. 10, 20, 30
b. 8, 10, 12
c. 5, 15, 45
d. 3, 6, 9

a)  LCM of   12, 10 ,   5  =   LCM  of   10, 20,  30

Step-by-step explanation:

The given set of numbers are 12, 10 and 5.

On prime factorization of the given numbers:

12  =  2 x 2 x 3

10  =  2 x  5

5   =   5 x 1

So, the LCM of the given set of number is 2 x 2 x 3 x 5  = 60

Now, find the LCM of each given set in the options.

a. 10, 20, 30

Here,  10  =  2 x  5   ,  20   =  2 x  2 x  5     ,  30    =    2 x  3 x  5

So, the LCM of the given set of number is   2 x 2 x 3 x 5  = 60

b. 8, 10, 12

Here,       8 =  2  x 2 x 2  ,   10  =  2 x  5   ,  12   =  2 x  2 x  3    

So, the LCM of the given set of number is 2 x 2 x 2 x 3 x 5  = 120

c. 5, 15, 45

Here,       5 =  5 x 1   ,   15  =   3 x 5 x 1   ,  45    =  3 x 3 x 5 x 1  

So, the LCM of the given set of number is   3 x 3 x 5  = 45

d. 3, 6, 9

Here,       3 =  3 x 1   ,   6  =  2 x 3 x 1     , 9    =  3 x 3  

So, the LCM of the given set of number is   2 x 3 x 3   = 18

a) Hence, here the LCM of   12, 10 and  5  = LCM of   10, 20   and 30 = 60