Answer:
5350 ml
Step-by-step explanation:
To find the size of the smallest container that will fill each of the packets and leave a remainder of 100 ml, we need to find the least common multiple (LCM) of the packet sizes (150 ml, 250 ml, and 350 ml) and then add 100 ml to it.
Let's find the LCM of 150, 250, and 350:
1. Prime factorize each number:
- \(150 = 2 \times 3 \times 5^2\)
- \(250 = 2 \times 5^3\)
- \(350 = 2 \times 5^2 \times 7\)
2. The LCM is the product of the highest powers of all prime factors involved:
LCM \(= 2^1 \times 3^1 \times 5^3 \times 7^1 = 2 \times 3 \times 5^3 \times 7 = 5250\)
Now, to leave a remainder of 100 ml, we add 100 ml to the LCM:
5250 + 100 = 5350
So, the size of the smallest container that will fill each of the packets and leave a remainder of 100 ml is 5350 ml.
