
Shortcut Trick
To find the least number of vessels, the capacity of each vessel must be the HCF of the given volumes.
HCF of 1755, 3783, 1599:
Difference between 1755 and 1599 = 156. Factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156.
Checking divisibility, HCF = 39 litres.
Total vessels = (1755 + 3783 + 1599) ÷ 39 = 7137 ÷ 39 = 183.
∴ The correct answer is 183 vessels.

Alternate Method

Given: Volumes are 1755 litres, 3783 litres, and 1599 litres.
Formula: Total Vessels = ∑(Volumes) ÷ HCF(Volumes)
⇒ Step 1: Find HCF using prime factorization or division method.
⇒ 1599 = 3 × 13 × 41
⇒ 1755 = 33 × 5 × 13
⇒ 3783 = 3 × 13 × 97
⇒ Common factors are 3 and 13. So, HCF = 3 × 13 = 39 litres.
⇒ Step 2: Calculate vessels for each type.
⇒ Vessels for Type 1 = 1755 ÷ 39 = 45
⇒ Vessels for Type 2 = 3783 ÷ 39 = 97
⇒ Vessels for Type 3 = 1599 ÷ 39 = 41
⇒ Total vessels = 45 + 97 + 41 = 183.
∴ The correct answer is 183 vessels.

Additional Information
HCF (Highest Common Factor)
The largest number that divides two or more numbers without leaving a remainder. For least number of containers, we always maximize the container size using HCF.
HCF by Difference Method
The HCF of a set of numbers is always a factor of the difference between any two numbers in the set.
LCM vs HCF in Word Problems
Use LCM when looking for a future common event (e.g., bells tolling together). Use HCF when dividing items into the largest possible equal groups.