Question
Find the HCF and LCM of 45, 60 and 75.
Solution
Prime factorization: 45 = 3² × 5 60 = 2² × 3 × 5 75 = 3 × 5² HCF: product of common prime factors with the smallest powers Common primes: 3 and 5 Smallest powers: 3¹, 5¹ HCF = 3 × 5 = 15 LCM: product of all prime factors with the highest powers Primes: 2, 3, 5 Highest powers: 2², 3², 5² LCM = 2² × 3² × 5² = 4 × 9 × 25 = 900 Answer: HCF = 15; LCM = 900.
Statement: T < U; W ≤ V = U; I > V; X ≥ U
Conclusion:
I. I > X
II. X ≥ I
Statements:
M < K ≤ G ≤ Z; P = J > Z; I ≥ R > P;
Conclusions:
I. K ≤ P
II. M < R
What should come in the place of question mark, in the given expressions to make ‘J < E’ always true?
‘D < E _? _F = G ≥ H = I ≥ J’
Which of the following makes C $ E or Y % E definitely true?
Statements: J > K = L ≥ M ≥ Q; N < O ≤ P < Q
Conclusions:
I. Q > N
II. J > O
Statement: N = P ≤ Q; R ≥ Q < U
Conclusions: I. N < U II. R ≥ N
...Statements: I > E ≥ F; G < D ≤ I; J < E ≤ H
Conclusions:
I. G < E
II. H ≥ F
III. E < D
Statements: Q > U = V ≤ X; R ≥ S ≥ X
Conclusions:
I. U = S
II. V < S
Statements:
A < R ≤ Y = F; U > L = T; A < L = P > E
Conclusions:
I). U > E
II). T > Y
...Statements: F % W, W © R, R @ M, M $ D
Conclusions:
 I.D @ R                               II.M $ F�...