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8 years, 5 months ago
The LCM of three positive integers X, Y and Z is 119^2. Find the total number of ordered triplets.
8 years, 1 month ago
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
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