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Giải Bài 127 trang 37 sách bài tập Toán 6 - Cánh diều

Tìm hai số tự nhiên a,b sao cho 0<a<b, a+b = 42 và BCNN(a,b) = 72.

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Đề bài

Tìm hai số tự nhiên a,b sao cho 0<a<b, a+b = 42 và BCNN(a,b) = 72.

Phương pháp giải - Xem chi tiết

BCNN(a,b) chia hết cho x thì a chia hết cho x hoặc b chia hết cho x

Lời giải chi tiết

Vì BCNN(a,b) = 72 chia hết cho 2 nên phải có ít nhất 1 trong 2 số a, b chia hết cho 2Không mất tính tổng quát, ta giả sử a chia hết cho 2.Vì a+b = 42 chia hết cho 2 nên b cũng chia hết cho 2Tương tự, vì BCNN(a,b) = 72 chia hết cho 3 nên phải có ít nhất 1 trong 2 số a, b chia hết cho 3Không mất tính tổng quát, ta giả sử a chia hết cho 3.Vì a+b = 42 chia hết cho 3 nên b cũng chia hết cho 3Như vậy, cả 2 số a,b đều chia hết cho 2, 3 nên a,b chia hết cho 6 hay a,b là bội của 6Mà 0<a<b, a+b = 42 và BCNN(a,b) = 72. Ta có bảng sau:
a 6 12 18
b 36 30 24
  Loại vì BCNN(a,b) = 36 Loại vì BCNN(a,b) =60 Thỏa mãn
Vậy a = 18 ; b = 24

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