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

Find the least number, which, when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34, respectively.
वह न्यूनतम संख्या ज्ञात कीजिए, जिसे 20, 25, 35 और 40 से विभाजित करने पर क्रमशः 14, 19, 29 और 34 शेष बचता है।

1238 1498 1389 1394

Detailed Solution & Logic

Correct Answer:

1394

20-14 = 6
25 -19 = 6
35 - 29 = 6
40 - 34 = 6
difference is 6
Now, the LCM of 20, 25, 35 and 40.
20 = \(2 \times 2 \times 5\)
25 = \(5\times 5\)
35= \(5\times 7\)
40 = \(2 \times 2 \times 2\times 5\)
Lcm = 1400
Required number = 1400 - 6 = 1394

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