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Answer:
given
AB*6=BBB
values of B B*6 unit digit
0 0*6 = 0 0
1 1*6 = 6 6
2 2*6 = 12 2
3 3*6 = 18 8
4 4*6 = 24 4
5 5*6 = 30 0
6 6*6 = 36 6
7 7*6 = 42 2
8 8*6 = 48 8
9 9*6 = 54 4
∴ B can be 0,2,4,6 and 8
for B=0
A0 * 6 = 000
which is not possible
so, B≠0
for B=2
A2 * 6 = 222
A2 = 222/6
A2 = 37
which is not possible
so, B≠2
for B=4
A4 * 6 = 444
A4 = 444/6
A4 = 74
so, A=7 and B=4
for B=6
A6 * 6 = 666
A6 = 111
which is not possible
so, B≠6
for B=8
A8 * 6 = 888
A8 = 148
which is not possible
so, B≠4
therefore A=7 and B=4
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