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Giải Bài 2.45 trang 55 SGK Toán 6 Kết nối tri thức với cuộc sống tập 1

Cho bảng sau:... a) Tìm các số thích hợp thay vào ô trống trong bảng; b) So sánh tích ƯCLN(a, b) . BCNN(a, b) và a.b. Em rút ra kết luận gì?

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

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Đề bài

Cho bảng sau:
a 9 34 120 15 2 987
b 12 51 70 28 1
ƯCLN(a,b) 3 ? ? ? ?
BCNN(a,b) 36 ? ? ? ?
ƯCLN(a,b) .BCNN(a,b) 108 ? ? ? ?
a.b 108 ? ? ? ?
a) Tìm các số thích hợp thay vào ô trống trong bảng; b) So sánh tích ƯCLN(a,b) . BCNN(a,b) và a.b. Em rút ra kết luận gì?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Tìm ƯCLN và BCNN của 2 số bằng cách phân tích 2 số ra thành tích các thừa số nguyên tố. Sau đó * Tìm ƯCLN: Ta chọn ra các thừa số nguyên tố chung, lập tích các thừa số vừa chọn, mỗi thừa số lấy với số mũ nhỏ nhất * Tìm BCNN: Ta chọn ra các thừa số chung và riêng, lập tích các thừa số đã chọn, mỗi thừa số lấy với số mũ lớn nhất

Lời giải chi tiết

a) Ta có bảng sau:
a 9 34 120 15 2 987
b 12 51 70 28 1
ƯCLN(a, b) 3

17

10

 1

1
BCNN(a, b) 36

102

840

 420

2 987
ƯCLN(a, b) .BCNN(a, b) 108

1 734

8 400

 420

2 987
a.b 108

1 734

8 400

 420

2 987
Giải thích:+) Ở cột thứ hai:a = 34 = 2.17; b = 51 = 3.17⇒ ƯCLN(a; b) = 17 ;  BCNN(a; b) = 2.3.17 = 102.ƯCLN(a, b) . BCNN(a, b) = 17.102 = 1 734.a.b = 34. 51 = 1 734.+) Ở cột thứ ba:a = 120 =\(2^3.3.5\) ;   b = 70 = 2.5.7⇒ ƯCLN(a, b) = 2. 5 = 10 ;  BCNN(a, b) =\(2^3.3.5.7\)= 840ƯCLN(a, b) . BCNN(a, b) = 10. 840 = 8 400.a.b = 120. 70 = 8 400.+) Ở cột thứ tư:a = 15 =3.5;   b =\(28 = 2^2.7\)⇒ ƯCLN(a, b) = 1 ;  BCNN(a, b) = \(2^2.3.5.7\)=420ƯCLN(a, b) . BCNN(a, b) =1. 420 = 420.a.b = 15. 28 = 420.+) Ở cột thứ năm:a = 2 987;   b = 1⇒ ƯCLN(a; b) = 1 ;  BCNN(a; b) = 2 987ƯCLN(a, b) . BCNN(a, b) = 1 . 2 987 = 2 987.a.b = 2 987 . 1 = 2 987
b) ƯCLN(a, b).BCNN(a, b) = a.b

💞Em rút ra kết luận: tích của BCNN và ƯCLN của hai số tự nhiên bất kì bằng tích của chúng.

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