2016 · Q41
Consider the following in respect of natural numbers a, b and c:
- 1LCM(ab, ac) = a·LCM(b, c);
- 2HCF(ab, ac) = a·HCF(b, c);
- 3HCF(a, b) < LCM(a, b);
- 4HCF(a, b) divides LCM(a, b).
Which of the above are correct?
Elementary MathematicsHCF and LCM
- A1 and 2 only
- B3 and 4 only
- C1, 2 and 4 only
- D1, 2, 3 and 4
Explanation
LCM(ab,ac) = a·LCM(b,c) and HCF(ab,ac) = a·HCF(b,c) are standard identities, and HCF always divides LCM — statements 1, 2, 4 true. Statement 3 fails when a = b (then HCF = LCM). Hence 1, 2 and 4 only, option C.