RS AGGARWAL HCF AND LCM IMPORTANT FACT AND FORMULAE-WWW.SHORCUTSPOT.CO.IN

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RS AGGARWAL'S
H.C.F AND L.C.M

Important facts & Formulae

I. Factors and Multiples.

If a number divides another number b exactly, we say that is a factor of b. In this case, b is called a multiple of A.

II.  Highest common  factor (HCF) or Greatest common measure (GCM) or greatest common devisor (GCD)

The HCF of two or more than two numbers is the greatest number that divides each of them exactly.
There are two methods of finding the HCF of a given set of numbers.

01. Factorization method:
Express each one of the given numbers as the product of prime factors. The product of least powers of common prime factors given HCF.

02. Division method :
Suppose we have to find the HCF of two given numbers, divide the larger number by smaller one. Now divide the devisor by the reminder. Repeat the process of dividing the proceeding number by the reminder last obtained till zero is obtained as reminder. The last divisor is the required HCF

Finding the HCF of more than  two numbers: Suppose we have to find the HCF of the three numbers. Then HCF of (HCF of any two) and (The third number) gives the HCF of three given numbers.
Similarly, The HCF  of more than three numbers may be obtained.

III. Least common multiple (LCM).
The lest number which is exactly divisible by each one of the given numbers is called their LCM.

01.  Factorization method of finding LCM
Resolve each of the given numbers into a product of prime factors. Then LCM is the product of highest powers of all the factors.

02. Common division method(Shortcut Method) of finding LCM.
Arrange the given numbers in a row in any order. Divide by a number which divides exactly at least two of the given numbers and carry forward the numbers  which are not divisible. Repeat the process till no two of the numbers are divisible by the same number except 1. The product of the divisors and the undivided numbers is the required LCM of the given numbers.

IV. Product of two numbers = Product of their HCF and LCM

V. Co-primes : Two number are said to be co-primes if their HCF is 1.

VI. HCF and LCM of fractions:

1. HCF  = (HCF of Numerators/LCM of Denominators).
2. LCM=  (LCM of Numerators/HCF of  Denominators)

VII. HCF and LCM of Decimal Fractions:
In given numbers, make the same number of decimal places by annexing zeros in some numbers, if necessary. Considering these numbers without decimal points, find HCF or LCM as the case may be. Now In the result, mark off as  many decimal places as are there in each of the given numbers.

VIII. Comparison of Fractions.

Find the LCM of the denominators of the given fractions. Convert each of the fractions into an equivalent fraction with LCM as the denominator, by multiplying both the numerator by same number. The resultant fraction with the greatest numerator is the greatest.