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 ofÂ 20,25,35Â andÂ 40,Â using prime factorization method

20=2Ã—2Ã—5

25=5Ã—5

35=5Ã—7

40=2Ã—2Ã—2Ã—5

LCMÂ (20,25,35,40)=1400

as per given statement we have to find the greatest number which when divided byÂ 20,25,35Â andÂ 40Â leaves remainder asÂ 14,19,29Â andÂ 34Â respectively.

i.e. less than Divisor in each case .

Required numberÂ =1400âˆ’6=1394......................(20âˆ’14=25âˆ’19=35âˆ’29=40âˆ’34=6)

1394Â is the required number.