Four bags can hold 30 kg, 54 kg, 65 kg and 72 kg of sugar Find the least amount of weight of sugar which can be put into exact number of small bags. Also find the number of small bags in which total amount of sugar is kept.
Answers
To find the least amount of weight of sugar that can be put into an exact number of small bags, we need to find the greatest common divisor (GCD) of the given weights. The GCD will represent the weight that can be evenly divided among the bags.
The weights given are 30 kg, 54 kg, 65 kg, and 72 kg. Let's find their GCD:
Step 1: Find the GCD of 30 kg and 54 kg:
30 kg = 2 × 3 × 5
54 kg = 2 × 3^3
The common factors are 2 and 3, so the GCD of 30 kg and 54 kg is 2 × 3 = 6 kg.
Step 2: Find the GCD of 6 kg (GCD of previous step) and 65 kg:
6 kg = 2 × 3
65 kg = 5 × 13
There are no common factors between 6 kg and 65 kg, so their GCD is 1 kg.
Step 3: Find the GCD of 1 kg (GCD of previous step) and 72 kg:
1 kg is a common factor of any number, so the GCD of 1 kg and 72 kg is 1 kg.Therefore, the least amount of weight of sugar that can be put into an exact number of small bags is 1 kg.
To find the number of small bags in which the total amount of sugar is kept, we divide the total weight of sugar (30 kg + 54 kg + 65 kg + 72 kg) by the GCD (1 kg):
Total weight of sugar = 30 kg + 54 kg + 65 kg + 72 kg = 221 kg
Number of small bags = Total weight of sugar / GCD = 221 kg / 1 kg = 221 bags
Therefore, the total amount of sugar can be kept in 221 small bags.