The LCM of three positive integers X, Y and Z is 119^2. Find the total number of ordered triplets.

Hi Diwas,

119^2 = 7^2 * 17^2 

Let (x, y, z) be the triplet

So, at least one number in this triplet must have 7^2 in it.

And, at least one number must have 17^2

Let's consider 7^2 

Let's find the number of triplets possible whose LCM = 7^2

(7^2, 7^0, 7^0) - 3 ways

(7^2, 7^1, 7^0) - 6 ways

(7^2, 7^1, 7^1) - 3 ways

(7^2, 7^2, 7^0) - 3 ways

(7^2, 7^2, 7^1) - 3 ways

(7^2, 7^2, 7^2) - 1 way

Total = 19 days

Similarly, we get 19 ways for 17^2

Therefore, total number of triplets possible = 19*19 = 361.

Hope this helps

Thanks