Question 20

“xyz” and “zyx” are three digit numbers where x, y, z are distinct digits from 0 to 9. Differenceof xyz and zyx has a factor of 7. What is the maximum possible value of the LCM of x, y and z?

Solution

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The difference between the numbers xyz and zyx will be a multiple of 99.

therefore, 99(x-z)= 99*7

x-z =7

So, there are two possibilities for x and z.

i) x = 9 and z = 2,

ii) x = 8 and z = 1

To maximize the LCM, the first case will be preferred.

Now, for maximum LCM, y will be maximum.

Let us check for y = 8.

LCM = 8*9 = 72

For y = 7, LCM = 7*2*9 = 126.

Therefore, maximum possible LCM=126

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