What is the least number which when divided by 3 5 6 8 10 and 12 leaves in each case a remainder 2 but when divided by 13 leaves no remainder?
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Solution:By option verification , 962 is divided by 3,5,6,8,10 and 12 leaves remainder 2, but when divided by 13 leaves no remainder (or) L.C.M of 3,5,6,8,10,12 is 120 1×120+2=122 is not divisible by 13 2×120+2=242 is not divisible by 13 3×120+2=362 is not divisible by 13 4×120+2=482 is not divisible by 13 5×120+2=602 is not divisible by 13 6×120+2=722 is not divisible by 13 7×120+2=842 is not divisible by 13 8×120+2=962 is divisible by 13  What is the least number which when divided by the number 3, 5, 6, 8, 10 and 12 leaves in each case a remainder 2 but when divided by 22 leaves no remainder ?A. 312 B. 242 C. 1562 D. 1586 Answer: Option B Solution(By Examveda Team)$$\eqalign{ & {\text{LCM of }}\left( {3,5,6,8,10,12} \right) \cr & = 3 \times 5 \times 2 \times 4 \cr & = 120 \cr & {\text{Required number is }} \cr & \frac{{120K + 2}}{{22}} = \frac{{10K + 2}}{{22}} \cr & {\text{at }}K{\text{ = 2,}}\frac{{10K + 2}}{{22}} \cr & \Rightarrow {\text{Remainder = 0}} \cr & {\text{The given condition satisfied}} \cr & {\text{ = }}120K + 2 \cr & = 240 + 2 \cr & = 242 \cr} $$ Click here to read 1000+ Related Questions on Problems on H.C.F and L.C.M(Arithmetic Ability)Given: The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3 The least number when divided by 9 remainder = 0 Concept Used: For the least number take LCM and also check that all conditions are satisfying or not For same remainder in each case add the remainder in the LCM Calculation: First we have to find the LCM of 5, 6, 7, 8 5 = 51 6 = 21 × 31 7 = 71 8 = 23 LCM of 5, 6, 7, 8 is 23 × 31 × 51 × 71 = 840 For same remainder we have to add 3 to the LCM ⇒ 840 + 3 Now check weather it is divisible by 9 or not 843/9 = Not divisible by 9 Now we have to take next multiple of LCM and then add 3 840 × 2 + 3 ⇒ 1683 Divide it by 9 1683/9 = 187 ⇒ 1683 is divisible by 9 ⇒ 1683 is the least number when divided by 5, 6, 7, 8 gives remainder 3 Shortcut Trick The least number must be divisible by 9 For divisibility of 9 sum of digits of the number must be divisible by 9 Checking it by options: Option 1) 1677 1 + 6 + 7 + 7 = 21 ⇒ 1677 is not divisible by 9 Option 2) 1683 1 + 6 + 8 + 3 = 18 ⇒ 1683 is divisible by 9 Option 3) 2523 2 + 5 + 2 + 3 = 12 ⇒ 2523 is not divisible by 9 Option 4) 3363 3 + 3 + 6 + 3 = 15 ⇒ 3363 is not divisible by 9 ∴ The least number is 1683 which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder. Latest MP Police Constable Updates Last updated on Sep 22, 2022 The Madhya Pradesh Police has released the revised schedule for the Preliminary Eligibility Test (PET) of the Madhya Pradesh Police Constable exam on 20th May 2022. The exam was cancelled in view of the extreme heatwave conditions in Madhya Pradesh. The PET is now scheduled for 6 June onwards. A total of 4000 vacancies are to be filled by the MP Police Constable Recruitment 2022. The candidates should go through the MP Police Constable Syllabus and Exam Pattern to have an idea of the requirements of the exam.
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Login Register now for special offers +91 Home > English > Class 14 > Maths > Chapter > Lcm & Hcf > What is the least number which... Updated On: 27-06-2022 UPLOAD PHOTO AND GET THE ANSWER NOW! Text Solution 31224215621586 Answer : B Answer Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams. 23273067 0 7.8 K वह न्यूनतम संख्या क्या है, जिससे 5,10,12 तथा 15 से भाग देने पर प्रत्येक स्थिति में 2 शेष बचता है लेकिन 7 से भाग देने पर कोई शेष नहीं बचता है ? 446654287 0 7.3 K 2:55 What is the least number which when divided by 8, 12 and 16 leaves 3 as the remainder in each case, but when divided by 7 leaves no any remainder? 646462972 0 3.3 K 2:15 The least number, which when divided by 5, 10, 12 and 15 leaves a remainder of 2, in each case but when divided by 7 leaves no remainder is 646640203 0 8.7 K 1:43 वह न्यूनतम संख्या क्या है जिसमे 6,8,10,12 और 14 से भाग देने पर प्रत्येक स्थिति में 2 शेषफल बचे ? 4379717 0 2.2 K 1:47 What is the least number which when divided by the numbers 3, 5, 6, 8, 10 and 12 leaves in each case a remainder 2 but when divided by 13 leaves no remainder? 646301786 0 900 1:51 What is the least number which when divided by the numbers 3,5,6,8,10 and 12 leaves in each case a remainder 2 but when divided by 13 leaves no remainder. Show More Comments Add a public comment... Follow Us: Popular Chapters by Class: Class 6 AlgebraBasic Geometrical IdeasData HandlingDecimalsFractions Class 7 Algebraic ExpressionsComparing QuantitiesCongruence of TrianglesData HandlingExponents and Powers Class 8 Algebraic Expressions and IdentitiesComparing QuantitiesCubes and Cube RootsData HandlingDirect and Inverse Proportions Class 9 Areas of Parallelograms and TrianglesCirclesCoordinate GeometryHerons FormulaIntroduction to Euclids Geometry Class 10 Areas Related to CirclesArithmetic ProgressionsCirclesCoordinate GeometryIntroduction to Trigonometry Class 11 Binomial TheoremComplex Numbers and Quadratic EquationsConic SectionsIntroduction to Three Dimensional GeometryLimits and Derivatives Class 12 Application of DerivativesApplication of IntegralsContinuity and DifferentiabilityDeterminantsDifferential Equations Privacy PolicyTerms And Conditions Disclosure PolicyContact Us What is the least number which on being divided by 5 6 8 9 12 leaves in each case a remainder 1 but when divided by 13 leaves no remainder?∴ The least number which is divided by 5, 6, 8, 9, 12 leaves a remainder 1 but when divided by 13 leaves no remainder is 3601. Option A is the correct option. What is the least number which on being divided by 5 10 12 and 15 leaves 2 as remainder in each case but if divided by 7 leaves no remainder?∴ The number is 64. When 5 8 and 12 divide a multiple of 13 the remainders left are 3 6 and 10 respectively find the least such number?Only one answer remains, 598. What is the least number when divided by 5 6 7 and 8 leaves a remainder 3?∴ The least number is 1683 which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder. What is the least number which when divided by 5 6 8 10 and 12?∴ The least number which is exactly divisible by 5, 6, 8, 10, and 12 is 120.
What is the least number which when divided by either 3 5 7 11 and 13 leaves a reminder of 1 in each case?This is Expert Verified Answer
The least number that leaves a "remainder 3" when divided by "5, 7 and 13" is 458.
What is the lowest number which leaves 3 as reminder when divided by 8 12 and 16?The correct option is A 51.
When 5 8 and 12 divide a multiple of 13 the remainders left are 3 6 and 10 respectively find the least such number?Only one answer remains, 598.
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