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Giải Bài 2.50 trang 55 SGK Toán 6 Kết nối tri thức với cuộc sống tập 1

Từ ba tấm gỗ có độ dài 56 dm, 48 dm và 40 dm, bác thợ mộc muốn cắt thành các thanh gỗ có độ dài như nhau mà không để thừa mẩu gỗ nào. Hỏi bác cắt như thế nào để được các thanh gỗ có độ dài lớn nhất có thể?

𝕴Tổng hợp đề thi học kì 2 lớp 6 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

ওTừ ba tấm gỗ có độ dài 56 dm, 48 dm và 40 dm, bác thợ mộc muốn cắt thành các thanh gỗ có độ dài như nhau mà không để thừa mẩu gỗ nào. Hỏi bác cắt như thế nào để được các thanh gỗ có độ dài lớn nhất có thể?

Phương pháp giải - Xem chi tiết

Độ dài 3 tấm phải chia hết cho độ dài thanh. Do đó độ dài mỗi thanh phải là ước chung của độ dài 3 thanh

Lời giải chi tiết

Các thanh gỗ có độ dài lớn nhất được cắt ra là ƯCLN(56, 48, 40)

Ta có: \(56=2^3.7\) 

\(48 = 2^4. 3\)\(40=2^3.5\)

⛄Ta thấy thừa số nguyên tố chung là 2 và có số mũ nhỏ nhất là 3

Do đó \(ƯCLN(56, 48, 40) =2^3\)Vậy chiều dài các thanh gỗ lớn nhất có thể cắt là 8 dm.

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