Find the greatest number of six digits which when divided by 24, 36, 60 and 90 leaves remainder 11 in each case. 6 अंकों की बड़ी से बड़ी संख्या ज्ञात कीजिए जो 24, 36, 60 और 90 से विभाजित करने पर प्रत्येक दशा में 11 शेषफल छोड़े।

We need the largest 6-digit number that leaves remainder 11 when divided by 24, 36, 60, and 90. First find LCM(24,36,60,90). 24 = 2³×3, 36 = 2²×3², 60 = 2²×3×5, 90 = 2×3²×5. LCM = 2³×3²×5 = 8×9×5 = 360. The required number is of form 360k + 11. Largest 6-digit number is 999999. 999999 ÷ 360 = 2777.77, so k = 2777. Number = 360×2777 + 11 = 999720 + 11 = 999731.