If you divide 28, 42 and 56 by a number, you can divide them exactly. The maximum number is______ All 12, 15 and 20 can divide the same natural number, which is the smallest______ .

If you divide 28, 42 and 56 by a number, you can divide them exactly. The maximum number is______ All 12, 15 and 20 can divide the same natural number, which is the smallest______ .

28 = 2 × 2 × 742 = 2 × 3 × 756 = 2 × 2 × 2 × 7, so the greatest common factor is: 2 × 7 = 14. Answer: the maximum number is 14. Decompose 12, 15 and 20 into prime factors: 12 = 2 × 2 × 3; 15 = 3 × 5; 20 = 2 × 2 × 5; the least common multiple of 12, 15 and 20 is: 2 × 2 × 3 × 5 = 60; answer: the minimum number is 60