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

A

Explanation:

Answer 2

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

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