Using the formula: HCF × LCM = Product of two numbers.

Therefore, 12 × LCM = 2160, so LCM = 2160 ÷ 12 = 180.

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.

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

Using HCF × LCM = Product of two numbers: 15 × 180 = 45 × other number.

Therefore, other number = 2700 ÷ 45 = 60.

144 = 2⁴ × 3². 196 = 2² × 7².

Common prime factors: 2².

Therefore, HCF = 4.

For co-prime numbers, HCF = 1.

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

Therefore, product = 221.

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

This is the smallest number divisible by all three.

Let numbers be 4k and 5k. HCF = k = 6.

Therefore, numbers are 24 and 30.

The larger number is 30.

56 = 2³ × 7, 84 = 2² × 3 × 7, 140 = 2² × 5 × 7.

Common prime factors: 2 × 7 = 14.

16 = 2⁴, 24 = 2³ × 3, 36 = 2² × 3². LCM = 2⁴ × 3² = 16 × 9 = 144.