Question

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

Answer 1

First find out the LCM of 20,25,35 and 40

20=2×2×5

25=5×5

35=1×5×7

40=2×2×2×5

LCM of 20,25,35 & 40 = 2×2×5×5×7×2=1400

So, $1400-6=1396$ will have a remainder $14,19,29,34$ when divided by $20,25,35,40$ respectively.

Alternate ways

when divided by 20,25,35,40 leaves a remainder 14,19,29,34
i.e 6 less than the divisor in each case

Hence the required number =1400−6=1394