Question

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

Answer 1

Answer:

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

Answer 2

Answer:

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

Hope it helps u ❤