Question

LCM of 3 natural numbers a,b,c is 150. If N is the number of such ordered triplet, then
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Answer 1

Question:

If the LCM of three natural numbers equals 150, then how many sets of three numbers are possible?

Answer:

19

Step-by-step explanation:

Well, lets first find factors of 150

150= 2*3*5*5

1,2,3,5,6,10,15,25,30,50,75,150

5 set LCM - 150 is LCM of 1,50,75,150, 30 .. 5C3 = 10

4 set LCM - 150 is LCM of 1,25,30,150..

4C3–1=3 (since 1,150,30 is already included above)

For 2,3,5,6,10 and 15 individually the LCM triplet pair is 150 and 1 .. = 6

Total triplets = 10+3+6=19

Answer 2

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