Tìm hai số tự nhiên a và b, biết rằng BCNN(a,b) = 150; ƯCLN(a,b) = 5.
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KD
1
NL
Nguyễn Lê Phước Thịnh
CTVHS
28 tháng 3
Ta có: \(a\cdot b=ƯCLN\left(a;b\right)\cdot BCNN\left(a;b\right)\)
=>\(a\cdot b=5\cdot150=750\)
ƯCLN(a;b)=5
=>a⋮5 và b⋮5
ab=750
mà a⋮5 và b⋮5
nên (a;b)∈{(5;150);(150;5);(10;75);(75;10);(15;50);(50;15);(25;30);(30;25)}
mà ƯCLN(a;b)=5
nên (a;b)∈{(5;150);(150;5);(10;75);(75;10);(15;50);(50;15);(25;30);(30;25)}
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
13 tháng 2
Câu a:
Gọi hai số cần tìm là: a; b
Theo bài ra ta có: a = 18d; b = 18k (d; k) = 1
18d + 18k = 162
18.(d+ k) = 162
d + k = 162 : 18
d + k = 9 và (d; k) =1
Ta có: (d; k) = (1; 8); (3; 6); (3; 6); (5; 4); (4; 5); (6; 3); (8; 1)
Vì (d; k) = (1; 8); (5; 4); (4; 5)
(a; b) = (18; 144); (90; 72); (72; 90)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
13 tháng 2
Câu b:
Theo bài ra ta có: a = 15d; b = 15k (d; k) = 1
15d.k = 300
d.k = 300 : 15
dk = 20
20 = 2^2.5; Ư(20) = {1; 2; 4; 5; 10; 20}
(d; k) = (1; 20); (2; 10); (4; 5); (5; 4); (10; 2); (20; 1)
Vì (d; k) = 1 nên (d; k) = (1; 20); (4; 5); (5; 4) ; (20; 1)
(a; b) = (15; 300); (60; 75); (75; 60); (300; 15)
8 tháng 12 2015
a) goi hai so la a ; b va a >b
vi UCLN(a,b)=18=>a=18k ; b=18q (trong do UCLN (k,q)=1 va k>q)
=>a+b=162
18k+18q =162
18(k+q)=162
k+q=9
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29 tháng 10 2016
21453
52542000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 542454550212.100000000000000000000000000000000000000000000000000000000000000000000000000000 |
3B
1
ƯCLN(a,b)=5
=>\(a=5\cdot x;b=5y\), với điều kiện là ƯCLN(x;y)=1
\(a\cdot b=5\cdot150=750\)
=>\(x\cdot y=30\)
Ta sẽ có bảng sau:
=>Các cặp số (a;b) cần tìm sẽ là (5;150); (150;5); (10;75); (75;10); (25;30); (30;25)