Quantitative Aptitude

20 = 2² × 5, 30 = 2 × 3 × 5, 40 = 2³ × 5. LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120.

45 = 3² × 5, 60 = 2² × 3 × 5, 75 = 3 × 5².

Common factors: 3 and 5. HCF = 3 × 5 = 15.

Using the formula: HCF × LCM = Product of two numbers. 15 × LCM = 2700, so LCM = 2700 ÷ 15 = 180.

Using Euclidean algorithm: 126 = 84 × 1 + 42, then 84 = 42 × 2 + 0.

Therefore, HCF(84, 126) = 42.

96 = 2⁵ × 3, 120 = 2³ × 3 × 5.

Common prime factors: 2³ × 3 = 8 × 3 = 24.

Consecutive even numbers differ by 2.

Examples: HCF(2,4)=2, HCF(6,8)=2, HCF(10,12)=2.

The HCF is always 2.

12 = 2² × 3, 15 = 3 × 5, 20 = 2² × 5. LCM = 2² × 3 × 5 = 60.

This is the smallest number divisible by all three.

For co-prime numbers, HCF = 1.

Using HCF × LCM = Product: 1 × 221 = Product.

Therefore, product = 221.

20 = 2² × 5, 30 = 2 × 3 × 5. LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60.

Factors of 18: 1, 2, 3, 6, 9, 18.

Factors of 27: 1, 3, 9, 27.

Common factors: 1, 3, 9.

Highest common factor = 9.