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What is the smallest multiple of 18 of the form 2A945B, where A and B are digits?

Sagot :

danielgeyfman

Answer:

[tex]219456[/tex]

Step-by-step explanation:

It must end in [tex]0,2,4,6,8[/tex] (divisible by 2 rule) and the digits must sum to a multiple of 9(divisible by 9 rule).

The digit sum is [tex]2+A+9+4+5+B=20+A+B[/tex].

We want to make [tex]A[/tex] as low as possible because it's a higher digit than [tex]B[/tex].

If [tex]A[/tex] is as low as possible, we have that the sum is [tex]20+0+7=27[/tex]. Uh-oh. [tex]B[/tex] has to be even! So [tex]A=0[/tex] doesn't work.

If [tex]A=1[/tex], we have that the sum is [tex]20+1+6=27[/tex]. Yay!

So, the answer is [tex]\boxed{219456}[/tex]

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