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Giải Bài 7 trang 58 SGK Toán 6 Cánh Diều Tập 1

Lịch cập cảng của ba tàu như sau: tàu thứ nhất cứ 10 ngày cập cảng một lần; tàu thứ hai cứ 12 ngày cập cảng một lần; tàu thứ ba cứ 15 ngày cập cảng một lần. Vào một ngày nào đó, ba tàu cùng nhau cập cảng. Sau ít nhất bao nhiêu ngày thì ba tàu lại cùng nhau cập cảng?

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Đề bài

Lịch cập cảng của ba tàu như sau: tàu thứ nhất cứ 10 ngày cập cảng một lần; tàu thứ hai cứ 12 ngày cập cảng một lần; tàu thứ ba cứ 15 ngày cập cảng một lần. Vào một ngày nào đó, ba tàu cùng nhau cập cảng. Sau ít nhất bao nhiêu ngày thì ba tàu lại cùng nhau cập cảng?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

- Số ngày giữa 2 lần cập cảng của tàu thứ nhất phải chia hết cho 10, của tàu thứ hai phải chia hết cho 12, của tàu thứ ba phải chia hết cho 15.

Lời giải chi tiết

Gọi: y là số ngày ít nhất mà ba tàu cập cảng cùng nhau. Khi đó y phải chia hết cho 10, 12, 15. Mà y là nhỏ nhất nên y là bội chung nhỏ nhất của 10, 12, 15. Ta có: 10 = 2 . 5 12 = \(2^2.3\) 15 = 3 . 5 => BCNN(10, 12, 15) = \(2^2 . 3 . 5 = 60\) Vậy: Sau ít nhất 60 ngày thì ba tàu lại cùng nhau cập cảng.

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