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