The smallest number when divided by 35, 45 and 55 leaves the remainder 17, 27 and 37 respectively is

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Given:

We need to find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively.

Concept used:

If difference between the given number and remainder remains same for each number, the required number will be the (LCM of the divisors - the constant difference)

Calculations:

Let us see the relation between the pairs of numbers if there is any:

20 - 14 = 6

25 -19 = 6

35 - 29 = 6

40 - 34 = 6.

The difference is 6

Now, the LCM of 20, 25, 35 and 40.

20 = 2 × 2 × 5

25 = 5 × 5

35 = 5 × 7

40 = 2 × 2 × 2 × 5

LCM = 1400

Required number = 1400 - 6 = 1394

The the required number is 1394.

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the least number such that, when it divided by 15, 25, 35 and 45. it leaves remainder 7, 17, 27 and 37 respectively is