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Giải Bài 5 trang 39 SGK Toán 6 Chân trời sáng tạo tập 1

Chị Lan có ba đoạn dây ruy băng màu khác nhau với độ dài lần lượt là 140 cm, 168 cm và 210 cm. Chị muốn cắt cả ba đoạn dây đó thành những đoạn ngắn hơn có cùng chiều dài để làm nơ trang trí mà không bị thừa ruy băng. Tính độ dài lớn nhất có thể của mỗi đoạn dây ngắn được cắt ra (độ dài mỗi đoạn dây ngắn là một số tự nhiên với đơn vị là xăng-ti-mét). Khi đó, chị Lan có được bao nhiêu đoạn dây ruy băng ngắn.

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Đề bài

Chị Lan có ba đoạn dây ruy băng màu khác nhau với độ dài lần lượt là 140 cm, 168 cm và 210 cm. Chị muốn cắt cả ba đoạn dây đó thành những đoạn ngắn hơn có cùng chiều dài để làm nơ trang trí mà không bị thừa ruy băng. Tính độ dài lớn nhất có thể của mỗi đoạn dây ngắn được cắt ra (độ dài mỗi đoạn dây ngắn là một số tự nhiên với đơn vị là xăng-ti-mét). Khi đó, chị Lan có được bao nhiêu đoạn dây ruy băng ngắn.

Phương pháp giải - Xem chi tiết

Độ dài lớn nhất có thể của mỗi đoạn dây ngắn được cắt ra chính là ước chung lớn nhất của 140, 168 và 210.

Lời giải chi tiết

- Độ dài lớn nhất có thể của mỗi đoạn dây ngắn được cắt ra chính là ƯCLN(140, 168, 210).- Ta có: 140 = \(2^2 .5.7\)168 = \(2^3.3.7\)210 =\( 2.3.5.7\)+Các thừa số nguyên tố chung là: 2 và 7+Số mũ nhỏ nhất của 2 là 1, của 7 là 1=> ƯCLN(140, 168, 210) = 2.7 = 14.=> Độ dài lớn nhất có thể của mỗi đoạn dây ngắn được cắt ra là 14 cm.- Tổng độ dài 3 đoạn dây của chị Lan là:140+168+210=518 (cm)- Số đoạn dây ruy băng ngắn chị Lan có được là:518 : 14 = 37 (đoạn dây).Vậy chị Lan có được 37 đoạn dây ruy băng ngắn.

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