There are three cans of milk containing 36 litres, 45 litres and 72 litres.…
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There are three cans of milk containing 36 litres, 45 litres and 72 litres. Find the biggest measure that can measure all these exactly .
Answer: A. 9 litres — Solution: Find the greatest measure that divides 36, 45 and 72 exactly. Prime factorization: 36 = 2 × 2 × 3 × 3 = 2^2 × 3^2; 45 = 3 × 3 × 5 = 3^2 × 5; 72 = 2…
- A.
9 litres
- B.
8 litres
- C.
7 litres
- D.
15 litres
Attempted by 204 students.
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Correct answer: A
Solution: Find the greatest measure that divides 36, 45 and 72 exactly.
Prime factorization: 36 = 2 × 2 × 3 × 3 = 2^2 × 3^2; 45 = 3 × 3 × 5 = 3^2 × 5; 72 = 2 × 2 × 2 × 3 × 3 = 2^3 × 3^2.
Common prime factors: 3 × 3 = 3^2 = 9.
Therefore the highest common factor (greatest measure) is 9 litres.
Check: 36 ÷ 9 = 4, 45 ÷ 9 = 5, 72 ÷ 9 = 8 — all whole numbers, so 9 litres measures all three exactly.