Oil volumes are 120 L, 180 L and 240 L. He fills equal-capacity tins to use all oil. What is the greatest capacity of a tin?
\(60\text{ L}\)
We are given three oil quantities: 120 L, 180 L, and 240 L.
We need to find the greatest capacity of a tin that can exactly fill each quantity without leaving any oil.
This means we need to find the Highest Common Factor (HCF) or Greatest Common Divisor (GCD) of 120, 180, and 240.
Step 1: Write the prime factors of each number.
\(120 = 2 \times 2 \times 2 \times 3 \times 5\)
\(180 = 2 \times 2 \times 3 \times 3 \times 5\)
\(240 = 2 \times 2 \times 2 \times 2 \times 3 \times 5\)
Step 2: Identify the common prime factors.
Step 3: Multiply the common factors.
\(2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60\)
Step 4: Therefore, the greatest capacity of each tin is \(60\text{ L}\).