Question

THE GREATEST NUMBER OF FIVE DIGITS WHICH WHEN DIVIDED BY 4,6,14 AND 20 LEAVES RESPECTIVELY 1,3,11 AND 17 AS REMAINDERS. THEN THE NUMBER WILL BE

Answer 1

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Answer 2

THE GREATEST NUMBER OF FIVE DIGITS WHICH WHEN DIVIDED BY 4,6,14 AND 20 LEAVES RESPECTIVELY 1,3,11 AND 17 AS REMAINDERS. THEN THE NUMBER WILL BE 99957

Solution:

The greatest number of 5 digit is 99999

Let us first find L.C.M of 4, 6, 14, 20:

List all prime factors for each number

Prime factorization of 4 = $2 \times 2$

Prime factorization of 6 = $2 \times 3$

Prime factorization of 14 = $2 \times 7$

Prime factorization of 20 = $2 \times 2 \times 5$

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new list is :

2, 2, 3, 5, 7

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 5 x 7 = 420

LCM(4, 6, 14, 20) = 420

When we divide 99999 by 420 we get remainder as 39

Now we have to subtract 39 from 99999 we get 99960

If we notice here, the difference between the divisor and the remainder is same in all cases which is 3

[ 4 -1 = 3 and 6 - 3 = 3 and 14- 11 = 3 and 20 - 17 = 3]

Now we subtract 3 from 99960 to get 99957

Hence the required 5 digit number is 99957

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