This question is taken from real numbers in which we have to find the least number which when divided by 20, 25, 35 and 40 leaves remainder 14, 19, 29 and 34 respectively.
Kindly solve the above problem in detail
RS aggarwal, Class 10, chapter 1B, question no 17
First LCM of 20,25,35 and 40, using prime factorization method
20=2×2×5
25=5×5
35=5×7
40=2×2×2×5
LCM (20,25,35,40)=1400
as per given statement we have to find the greatest number which when divided by 20,25,35 and 40 leaves remainder as 14,19,29 and 34 respectively.
i.e. less than Divisor in each case .
Required number =1400−6=1394......................(20−14=25−19=35−29=40−34=6)
1394 is the required number.