Respuesta :
Answer:
Step-by-step explanation:
given that a and b are two positive integers
gcd(a,b)=210, lcm[a,b]=210^3,
We know that gcd divides both a and b.
and lcm is divisible by both a and b.
Also the product of a and b is the product of lcm and gcd
i.e. [tex]ab = 210(210)^3\\=210^4[/tex]
a= 210x and b = 210y where
ab = 210^4
i.e. xy = 210^3
Possible pairs are
The factor pairs of 9,261,000 are:
1 × 9261000 = 9,261,000
2 × 4630500 = 9,261,000
3 × 3087000 = 9,261,000
4 × 2315250 = 9,261,000
5 × 1852200 = 9,261,000
6 × 1543500 = 9,261,000
7 × 1323000 = 9,261,000
8 × 1157625 = 9,261,000
9 × 1029000 = 9,261,000
10 × 926100 = 9,261,000
12 × 771750 = 9,261,000
14 × 661500 = 9,261,000
15 × 617400 = 9,261,000
18 × 514500 = 9,261,000
20 × 463050 = 9,261,000
21 × 441000 = 9,261,000
24 × 385875 = 9,261,000
25 × 370440 = 9,261,000
27 × 343000 = 9,261,000
28 × 330750 = 9,261,000
30 × 308700 = 9,261,000
35 × 264600 = 9,261,000
36 × 257250 = 9,261,000
40 × 231525 = 9,261,000
42 × 220500 = 9,261,000
45 × 205800 = 9,261,000
49 × 189000 = 9,261,000
50 × 185220 = 9,261,000
54 × 171500 = 9,261,000
56 × 165375 = 9,261,000
60 × 154350 = 9,261,000
63 × 147000 = 9,261,000
70 × 132300 = 9,261,000
72 × 128625 = 9,261,000
75 × 123480 = 9,261,000
84 × 110250 = 9,261,000
90 × 102900 = 9,261,000
98 × 94500 = 9,261,000
100 × 92610 = 9,261,000
105 × 88200 = 9,261,000
108 × 85750 = 9,261,000
120 × 77175 = 9,261,000
125 × 74088 = 9,261,000
126 × 73500 = 9,261,000
135 × 68600 = 9,261,000
140 × 66150 = 9,261,000
147 × 63000 = 9,261,000
150 × 61740 = 9,261,000
168 × 55125 = 9,261,000
175 × 52920 = 9,261,000
180 × 51450 = 9,261,000
189 × 49000 = 9,261,000
196 × 47250 = 9,261,000
200 × 46305 = 9,261,000
210 × 44100 = 9,261,000
216 × 42875 = 9,261,000
225 × 41160 = 9,261,000
245 × 37800 = 9,261,000
250 × 37044 = 9,261,000
252 × 36750 = 9,261,000
270 × 34300 = 9,261,000
280 × 33075 = 9,261,000
294 × 31500 = 9,261,000
300 × 30870 = 9,261,000
315 × 29400 = 9,261,000
343 × 27000 = 9,261,000
350 × 26460 = 9,261,000
360 × 25725 = 9,261,000
375 × 24696 = 9,261,000
378 × 24500 = 9,261,000
392 × 23625 = 9,261,000
420 × 22050 = 9,261,000
441 × 21000 = 9,261,000
450 × 20580 = 9,261,000
490 × 18900 = 9,261,000
500 × 18522 = 9,261,000
504 × 18375 = 9,261,000
525 × 17640 = 9,261,000
540 × 17150 = 9,261,000
588 × 15750 = 9,261,000
600 × 15435 = 9,261,000
630 × 14700 = 9,261,000
675 × 13720 = 9,261,000
686 × 13500 = 9,261,000
700 × 13230 = 9,261,000
735 × 12600 = 9,261,000
750 × 12348 = 9,261,000
756 × 12250 = 9,261,000
840 × 11025 = 9,261,000
875 × 10584 = 9,261,000
882 × 10500 = 9,261,000
900 × 10290 = 9,261,000
945 × 9800 = 9,261,000
980 × 9450 = 9,261,000
1000 × 9261 = 9,261,000
1029 × 9000 = 9,261,000
1050 × 8820 = 9,261,000
1080 × 8575 = 9,261,000
1125 × 8232 = 9,261,000
1176 × 7875 = 9,261,000
1225 × 7560 = 9,261,000
1260 × 7350 = 9,261,000
1323 × 7000 = 9,261,000
1350 × 6860 = 9,261,000
1372 × 6750 = 9,261,000
1400 × 6615 = 9,261,000
1470 × 6300 = 9,261,000
1500 × 6174 = 9,261,000
1512 × 6125 = 9,261,000
1575 × 5880 = 9,261,000
1715 × 5400 = 9,261,000
1750 × 5292 = 9,261,000
1764 × 5250 = 9,261,000
1800 × 5145 = 9,261,000
1890 × 4900 = 9,261,000
1960 × 4725 = 9,261,000
2058 × 4500 = 9,261,000
2100 × 4410 = 9,261,000
2205 × 4200 = 9,261,000
2250 × 4116 = 9,261,000
2450 × 3780 = 9,261,000
2520 × 3675 = 9,261,000
2625 × 3528 = 9,261,000
2646 × 3500 = 9,261,000
2700 × 3430 = 9,261,000
2744 × 3375 = 9,261,000
2940 × 3150 = 9,261,000
3000 × 3087 = 9,261,000
