# Maths Science Corner

# Maths

## Daily Quiz

# LCM and HCF

# Paper Set 14

These posts are made precisely to give you the best shortest possible solution of all the questions.

Solutions cover variety of topics which are listed below :

**Mathematics**

Number System

LCM and HCF

Simplification

Power, Indices and Surds

Average

Ratio and Proportion

Percentage

Profit and Loss

Discount

Simple Interest

Compound Interest

Time and Work

Pipe and Cistern

Time and Distance

Boat and Stream

Sequence and Series

Algebra

Trigonometry

Geometry

Mensuration (2 - D and 3 - D)

Statistics and Data interpretation

**Reasoning**

Analogy or Similarity

Blood Relationship

Symbols and Notations

Classification

Direction and Distance tests

Schedule day/date/time

Series

Coding - Decoding

Word formation

Syllogism, Statement and Conclusions

Ranking and Arrangement

Finding the missing Number

Arithmetical problems

Arrangement of words in logical order

Cubes and Dice

Logical Venn Diagram

Series

Mirror Images

Water Images

Paper cutting and folding

Completion of figures

Embedded Figure

Deviation of figure

We will try to cover above all types of questions. So, keeping in touch with us will give you chance to crack various Government and Other Exams.

__Points to Remember for LCM and HCF__Important Definitions :

Highest Common Factor (H.C.F) : It is also called Greatest common Diviser (G.C.D). When a greatest number divides perfectly the two or more given numbers then that number is called the H.C.F. of two or more given numbers.

e.g. The H.C.F of 10, 20, 30 is 10 as they are perfectly divided by 10,5 and 2 and 10 is highest or greatest of them.

Least common Multiple (L.C.M.) : The least number which is divisible by two or more given numbers, that least number is called L.C.M. of the numbers. L.C.M. of 3,5,6 is 30, because all 3 numbers divide 30, 60, 90, ...... and so on perfectly and 30 is minimum of them.

Factor and Multiple : If a number m, divides perfectly second number n, then m is called the factor of n and n is called the multiple of m.

Rule 1 : 1st number × 2nd number = L.C. M. × H.C.F.

There are two methods for calculating the H.C.F and L.C.M.

(i) Factor Method

(ii) Division Method

If the ratio of two numbers is a:b, (lowest form i.e. indivisible to each other) then Numbers are ak and bk, where k is a constant and hence, H.C.F. is K and L.C.M. is abk.

Rule 2 : L.C.M of fractions = L.C.M.of numerators / H.C.F.of denominators

Rule 3 : H.C.F. of fractions = H.C.F of numerators / L.C.M.of denominators

IMPORTANT POINTS

If there is no common factor between two numbers, then L.C.M. will be the product of both numbers.

If there are ‘n’ numbers in a set and H.C.F. of any two numbers is H and L.C.M. of all ‘n’ numbers is L, then product of all ‘n’ numbers is (H)n-1 ´ L

Rule 4 : When a number is divided by a, b or c leaving same remainder ‘r’ in each case then that number must be k + r where k is LCM of a, b and c.

Rule 5 : When a number is divided by a, b or c leaving remainders p, q or r respectively such that the difference between divisor and remainder in each case is same i.e., (a – P) = (b – q) = (c – r) = t (say) then that (least) number must be in the form of (k – t), where k is LCM of a, b and c

Rule 6 : The largest number which when divide the numbers a, b and c the remainders are same then that largest number is given by H.C.F. of (a – b), (b – c) and (c – a).

Rule 7 : The largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).

Rule 8 : Greatest n digit number which when divided by three numbers p,q,r leaves no remainder will be, Required Number = (n – digit greatest number) – R

Where R is the remainder obtained on dividing greatest n digit number by L.C.M of p.q,r.

Rule 9 : The n digit largest number which when divided by p, q, r leaves remainder ‘a’ will be

Required number = [n – digit largest number – R] + a

where, R is the remainder obtained when n – digit largest number is divided by the L.C.M of p, q, r.Today we are going to give you the Paper Set of #LCM_HCF question of #Dailyquiz in #Maths asked earlier in various competitive Examinations. Yoy can follow Maths Science Corner on Facebook page, Twitter and Telegram. Enjoy the Paper Set and keep learning.

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