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Giải Bài 2.63 trang 46 sách bài tập Toán 6 Kết nối tri thức với cuộc sống

Biết hai số 2^3.3^a và 2^b.3^5 có ước chung lớn nhất là 2^2.3^5 và bội chung nhỏ nhất là 2^3.3^6. Hãy tìm giá trị của các số tự nhiên a và b.

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

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Đề bài

Biết hai số 23.3a và 2b.35 có ước chung lớn nhất là 22.35 và bội chung nhỏ nhất là 23.36. Hãy tìm giá trị của các số tự nhiên a và b.

Phương pháp giải - Xem chi tiết

*Sử dụng kết quả a.b= ƯCLN(a,b). BCNN(a,b)

Lời giải chi tiết

Gọi x = 23.3a  và y = 2b.35

Ta có: x. y = ƯCLN(x, y). BCNN(x, y)

Vì ước chung lớn nhất của hai số là 22.35 và bội chung nhỏ nhất của hai số là 23.36

Ta được x.y= \(2^2.3^5.2^3.3^6=2^2.2^3.3^5.3^6=2^5. 3^{11}\)Mà xy =\(2^{3+b}.3^{a+5}\)Ta được 5=3+b và 11=a+5Vậy b=2 và a=6

 Lời giải hay

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