A number when divided by 12, 15 and 18 leaves remainders 5, 8 and 11 respectively. Find the least positive number satisfying all these conditions.किसी संख्या को 12, 15 तथा 18 से विभाजित करने पर क्रमशः 5, 8 तथा 11 शेषफल प्राप्त होते हैं। इन सभी शर्तों को संतुष्ट करने वाली सबसे छोटी धनात्मक संख्या ज्ञात कीजिए।
Correct answer: 173
Explanation: Since the remainders are 7 less than the respective divisors:
12 − 7 = 5
15 − 7 = 8
18 − 7 = 11
Therefore, the number + 7 must be divisible by 12, 15 and 18.
LCM(12, 15, 18) = 180
Therefore:
Number + 7 = 180
Number = 180 − 7 = 173
Final Answer: 173
12 − 7 = 5
15 − 7 = 8
18 − 7 = 11
Therefore, the number + 7 must be divisible by 12, 15 and 18.
LCM(12, 15, 18) = 180
Therefore:
Number + 7 = 180
Number = 180 − 7 = 173
Final Answer: 173