(a) 115(6) 23674. What is the least number which when divided by 20, 2

1.	(a) 115(6) 23674. What is the least number which when divided by 20, 25, 35, 40 leavesrespectively 14, 19, 29, 34 as a remainder?(d) 1664
Answer» 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=1400when divided by 20,25,35,40 leaves a remainder 14,19,29,34i.e 6 less than the divisor in each case Hence the required number =1400−6=1394

(a) 115(6) 23674. What is the least number which when divided by 20, 25, 35, 40 leavesrespectively 14, 19, 29, 34 as a remainder?(d) 1664

Answer»

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=1400when divided by 20,25,35,40 leaves a remainder 14,19,29,34i.e 6 less than the divisor in each case

Hence the required number =1400−6=1394