In a store, there are 345 L mustard oil, 120 L sunflower oil and 225 L soyabean oil. What will be the capacity of the largest container to measure the above three types of oil?

Options

A. 8L
B. 20 L
C. 23 L
D. 15 L

Answer

To find the capacity of the largest container that can measure the three types of oil (mustard oil, sunflower oil, and soyabean oil), we need to determine the highest common factor (HCF) of the three quantities: 345 L, 120 L, and 225 L.

### Step-by-Step Solution:

**Step 1: Find the prime factorization of each quantity.**

- For 345:
- Divide by 3: \( 345 ÷ 3 = 115 \)
- Divide by 5: \( 115 ÷ 5 = 23 \)
- 23 is a prime number.
- So, the prime factorization of 345 is \( 3^1 × 5^1 × 23^1 \).

- For 120:
- Divide by 2: \( 120 ÷ 2 = 60 \)
- Divide by 2: \( 60 ÷ 2 = 30 \)
- Divide by 2: \( 30 ÷ 2 = 15 \)
- Divide by 3: \( 15 ÷ 3 = 5 \)
- 5 is a prime number.
- So, the prime factorization of 120 is \( 2^3 × 3^1 × 5^1 \).

- For 225:
- Divide by 3: \( 225 ÷ 3 = 75 \)
- Divide by 3: \( 75 ÷ 3 = 25 \)
- Divide by 5: \( 25 ÷ 5 = 5 \)
- 5 is a prime number.
- So, the prime factorization of 225 is \( 3^2 × 5^2 \).

**Step 2: Identify the common prime factors.**

- The common prime factors from the factorizations are:
- For 3: The minimum power is \( 3^1 \) (from 345 and 120).
- For 5: The minimum power is \( 5^1 \) (from all three).

**Step 3: Calculate the HCF.**

- HCF = \( 3^1 × 5^1 = 3 × 5 = 15 \).

**Step 4: Conclusion.**

- The capacity of the largest container that can measure all three types of oil is **15 liters**.