Study Material on Quantitative Aptitude for SSC Combined Graduate Level Exam: H.C.F. & L.C.M

Quantitative Segment Questions are framed to test how capable are the aspirants in appropriately using numbers. The scope of the test will be computation of whole numbers, decimals, fractions & relationships between numbers; percentage & ratio, time & distance; profit, loss & discount; graphs of linear equations; basic algebraic identities; pie chart; trigonometric ratio, geometry etc.

If a number x divides another number y exactly, then x is said to be a factor of y. To add, subtract, or just compare two fractions, we need to convert both fractions to a common denominator. The least common multiple is usually used, although any common multiple would work in this particular case.

Explaining the concept of Least Common Multiple (L.C.M.) & Highest common Factor (H.C.F)

Least Common Multiple (L.C.M.):- The least number which is exactly divisible by each one of the given numbers is called their L.C.M.

Also to simplify a fraction, we divide the numerator and the denominator by the same number. If we divide them by the greatest common factor, then no further simplifications are required. That greatest common factor is called the Highest Common Factor (H.C.F.) or Greatest Common Divisor. The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly.

Important Formulas of L.C.M. and H.C.F. of Numbers –

Product of two numbers =Product of their H.C.F and L.C.M.

 H.C.F.=(H.C.F.of Numerators)/(L.C.M.of Denominators)

 L.C.M=(L.C.M.of Numerators)/(H.C.F.of Denominators)

Example:-The L.C.M. and H.C.F. of two numbers are 3 and 105 respectively. If the sum of these numbers is 36, then what is the sum of the reciprocals of the numbers?

Solution:-We will solve this problem in to steps

Step I:-
Suppose the first number = X
And the second number = Y
Step II:-
According to the given example
L.C.M. of two numbers = 3
H.C.F of two numbers = 105
Then,
       L.C.M. × H.C.F. = 3 × 105
                    X × Y    = 3 × 105

    [Because we know that, If X and Y are two numbers then 
     (L.C.M. of X and Y) × (H.C.F. of X and Y) =X × Y]
                    X × Y    = 315 ______________ (1)
Step III:- 
Also given in the example   
    
                    X + Y = 36 _______________ (2)
Step IV:-
From step II and step III
( X + Y )/(X × Y)  =36/315

 X/(X × Y) + Y/(X × Y) = 36/315

    1/Y   +  1/X     = 4/35

    1/X   +  1/Y     = 4/35

Hence, the sum of the reciprocals of two numbers X and Y is  4/35.