Consider the following statements : 1. If a = be with HCF (b, c) = l then HCF (c, bd) = HCF (c, d). 2. If a = be with HCF (b, c) = 1, then LCM (a, d) = LCM (c, bd). Which of the above statements is/are correct ?

CDS 2017 PYQ with Answer — Consider the following statements : 1. If a = be with HCF (b, c) = l…

2017 · Q4

Consider the following statements :

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

Which of the above statements is/are correct ?

Elementary MathematicsHCF and LCM

A1 only
B2 only
CBoth 1 and 2
DNeither 1 nor 2

Explanation

(Reading the transcribed 'a = be' as the standard a = bc, and 'HCF(b,c) = l' as 1.) Statement 1 is true: with a = bc and HCF(b,c) = 1, any common divisor of c and bd is coprime to b, hence divides d, so HCF(c,bd) = HCF(c,d). Statement 2 is false — e.g. b = 2, c = 3, d = 6 gives LCM(a,d) = LCM(6,6) = 6 but LCM(c,bd) = LCM(3,12) = 12. So only statement 1 is correct: option A.