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.

HCF × LCM = Product of numbers. 18 × 324 = 36 × other.

Therefore, other = 5832 ÷ 36 = 162.

Consecutive even numbers differ by 2.

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

The HCF is always 2.

110 = 2 × 5 × 11, 165 = 3 × 5 × 11, 220 = 2² × 5 × 11.

Common factors: 5 × 11 = 55.

For 28 and 35: HCF = 7, LCM = 140.

Verify: 28 = 2² × 7, 35 = 5 × 7. HCF = 7, LCM = 2² × 5 × 7 = 140. ✓

108 = 2² × 3³, 135 = 3³ × 5, 162 = 2 × 3⁴. LCM = 2² × 3⁴ × 5 = 4 × 81 × 5 = 1620.

Wait, recalculating: 2² × 3⁴ × 5 = 4 × 81 × 5 = 1620.

But checking 135: 3³ × 5, so LCM = 2² × 3⁴ × 5 = 1620.

Actually, LCM should be 1620.

Let me verify with 1080: 1080 = 2³ × 3³ × 5.

Testing divisibility and checking again: LCM = 1080.

96 = 2⁵ × 3, 120 = 2³ × 3 × 5.

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