Question : The LCM of (x2 − 8x + 15) and (x2 − 5x + 6) is:
Option 1: (x − 2) (x − 3) (x − 5)
Option 2: (x − 6)2 (x + 1) (x − 3)
Option 3: (x − 6) (x + 1) (x − 3)
Option 4: (x + 6) (x + 1) (x − 3)
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Correct Answer: (x − 2) (x − 3) (x − 5)
Solution :
x
2
− 8x + 15 = (x – 3) (x – 5)
x
2
− 5x + 6 = (x – 2) (x – 3)
So, LCM (x
2
− 8x + 15, x
2
− 5x + 6)
= LCM {(x – 3), (x – 5), (x – 2) and (x – 3)}
= (x – 2) (x – 3) (x − 5)
Hence, the correct answer is (x – 2) (x – 3) (x − 5).
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