Solution: According to the formula, 1st number × 2nd number = HCF × LCM. 36 × 2nd number = 12 × 180 ⟹ 2nd number =12×180/ 36= 60.

Solution: Let us divide the options by the HCF (8): 24 ÷ 8 = 3 (Divisible) 48 ÷ 8 = 6 (Divisible) 56 ÷ 8 = 7 (Divisible) 60 ÷ 8 = 7.5 (Not completely divisible, so it cannot be the LCM)

Solution: Subtract 12 from each number: 1356 − 12 = 1344, 1868 − 12 = 1856, 2764 − 12 = 2752. Now we find the HCF of the mutual differences of these numbers: 1856 − 1344 = 512, 2752 − 1856 = 896. HCF(512,896) = 156.

Solution: Find the LCM of 9, 12, and 15: 9 = 3×3, 12 = 2×2 × 3, 15 = 3 × 5. LCM = 2×2 ×3×3× 5=4 × 9 × 5 = 180 minutes. Converting minutes into hours: 180 ÷ 60 = 3 hours.

Solution: LCM(3,4,5,6,8) = 120. Prime factorization of 120 = 2×3 × 3 × 5. To make it a perfect square, multiply by the unmatched prime factors (2,3,5), which gives 2 × 3 × 5 = 30. Required square number = 120 × 30 = 3600.