Consider the following statements 1 If a bc with HCF b c 1 then HCF c bd HCF c d 2 If a bc with HCF ...........

Quantitative Aptitude (CDS) LCM, HCF

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Consider the following statements :

1. If a = bc with HCF (b, c) = 1, then HCF (c, bd) = HCF (c, d).

2. If a = bc with HCF (b, c) = 1,then LCM (a, b) = LCM (c, bd).

Which of the above statements is/are correct?

Only 1

Only 2

Both 1 and 2

Neither 1 nor 2

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Explanation:

We can solve this question by taking arbitrary values
As a = b × c
Let a = 6, b = 2, c = 3
Statement 1:
HCF(3, 2 × 6)
= HCF(3, 12) = 3
HCF(3, 6) = 3
Hence statement 1 is correct.
Statement 2:
LCM(6, 6) = 6
LCM(3, 12) = 12
i.e. LCM(6, 6) ≠ LCM(3, 12)
Hence statement 2 is incorrect.