2024 · Q36
Let n be a natural number. The HCF of n, n + 10 is 10. If the LCM is x (a 2 - digit number), then how many values of x are possible?
Elementary MathematicsHCF and LCM
- AOnly one
- BOnly two
- COnly three
- DMore than three
Explanation
HCF(n, n+10) = 10 forces n = 10k. Then LCM = n(n+10)/10 = 10k(k+1) = x, a 2-digit number. k(k+1) ≤ 9 admits k = 1 (x = 20) and k = 2 (x = 60) only. Two values are possible — option B.