Using HCF × LCM = Product of numbers: 4 × 60 = 20 × other.

Therefore, other = 240 ÷ 20 = 12.

Let numbers be 2k, 3k, 4k. HCF = k = 5.

Numbers are 10, 15, 20.

Sum = 10 + 15 + 20 = 45.

12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. LCM = 2³ × 3² = 72.

Smallest 4-digit multiple: ⌈1000 ÷ 72⌉ × 72 = 14 × 72 = 1008.

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

Therefore, HCF(84, 126) = 42.

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

Using HCF × LCM = Product of numbers: 12 × 72 = 24 × other number. 864 = 24 × other number.

Other number = 864 ÷ 24 = 36.

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

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

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

HCF × LCM = Product of numbers. 12 × 144 = 36 × other. 1728 = 36 × other.

Other = 1728 ÷ 36 = 48.

150 = 2 × 3 × 5², 200 = 2³ × 5².

Common factors: 2 and 5². HCF = 2 × 5² = 2 × 25 = 50.