Quantitative Aptitude Important Formulas

H.C.F and L.C.M - Important Formulas,Tricks and Examples

Factors and Multiples: If a number x divides another number y exactly, we say that x is a factor of y. Also y is called a multiple of x.

Highest Common Factor (HCF)
The H.C.F. of two or more than two numbers is the greatest number that divides each one of them exactly. There are two methods for determining H.C.F.:

Prime factorization method
Step 1: Express each number as a product of prime factors.
Step 2: HCF is the product of all common prime factors using the least power of each common prime factor

Division Method
Step 1: Write the given numbers in a horizontal line separated by commas.
Step 2: Divide the given numbers by the smallest prime number (write in the left side) which can exactly divide all the given numbers.
Step 3: Write the quotients in a line below the first.
Step 4: Repeat the process until we reach a stage where no common prime factor exists for all the numbers.
Step 5: We can see that the factors mentioned in the left side clearly divides all the numbers exactly and they are common prime factors. Their product is the HCF


Lowest Common Multiple (LCM)
The L.C.M. of two or more than two numbers is the least number which is exactly divisible by each one of the given numbers.

Prime factorization method
Step 1 : Express each number as a product of prime factors.
Step 2 : LCM is The product of highest powers of all prime factors.

Division Method
Step 1: Write the given numbers in a horizontal line separated by commas.
Step 2: Divide the given numbers by the smallest prime number which can exactly divide at least two of the given numbers.
Step 3: Write the quotients and undivided numbers in a line below the first.
Step 4: Repeat the process until we reach a stage where no prime factor is common to any two numbers in the row.
Step 5: LCM is The product of all the divisors and the numbers in the last line.

HCF and LCM of Fractions
LCM of fractions =LCM of Numerators/HCF of Denominators
HCF of fractions =HCF of Numerators/LCM of Denominators

Note:
Product of two numbers = Product of their HCF and LCM.

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Ratio and Proportion

A certain sum of money is divided between A and B in the ratio of 5/4 : 5/3 and A got Rs. 360/-. Find the total sum of money and B’s share?

In an office, the ratio of the salaries of an officer and a clerk is 15:7. If the salary of a clerk is Rs. 720/- less than the salary of the officer, find the salary of each?

In an election to a municipal council, the votes secured by two candidates are in the ratio 13:19. The elected candidates gets 312 votes more than the second candidate. How many votes are secured by the second candidate?

A certain sum of money is divided between Murthy and Prasad in the ratio 22/7 : 8/3. If Murthy gets Rs. 120/- more than Prasad, find the share of each?

In a cricket test series, the runs made by Raju and Tendulkar are in the ratio 5:9 and Tendulkar and Azar are in the ratio 6:7. What are the runs made by them if Azar makes 187 runs more than Raju?

If A:B = 2:3 and B:C = 9:5 find A:B:C?

If A:B = 3/5:5/7 and B:C = 3/4:2/5, find A:B:C?

If R:S = 0.01:0.11 and S:T = 2.2:1, Find R:S:T?

In a school, Under a Saving Scheme, Rekha saves 3/2 times the savings of Bindu, Geeta saves 4 times the savings of Rekha. Find the ratio of the savings of all the three in least terms?

Simplification

A man left 1/3 rd of his property to his wife and 3/5 th of the remainder to his daughter. He gave the rest to his son who received Rs. 6400/-. How much was his original property worth?

Ratio and Proportion

In a school 4/9 of the pupils are boys. There are 125 girls. How many boys are there?

If A:B = 3:4 and B:C = 5:6, find A:C?

IF X:Y = 3:4 AND Y:Z = 4:5, FIND X:Y:Z?

Area

A house site is in the shape of a square. Its area is 1225 sq metres. What is its perimeter?

The area of a square field is 7396 sq metres. Find its perimeter?

Numbers

Twice the first of three consecutive even integer is 6 more than the second integer. What is the third integers?

Ratio and Proportion

If 2x=3y and 4y=5z, then what is x:z=?

What quantity must be added to each term of the ratio a + b : a – b to make it equal to (a + b)2 : (a – b)2 ?