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Question

The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19, 29 and 34 respectively, is 1394. How?

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Solution

In this type of questions , we first find LCM of given numbers and then subtract common value to get the answer.

Common value = Number - Remainder
So,
20–14 =6
25–19=6
35–29=6
40–34 = 6

Now LCM of 20, 25, 35 and 40 -

20 = 2^2 * 5

25 = 5^2

35 = 5*7

40 = 2^3 * 5

therefore LCM = 2^3 * 5^2 * 7 = 1400

As i wrote above to get the final answer we have to subtract common value from LCM.

Final answer = 1400 - 6 = 1394


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