Important Formula: HCF & LCM

# Important Formula: HCF & LCM | Quantitative Aptitude for SSC CGL PDF Download

 Table of contents HCF and LCM Formula How to find HCF HCF by Prime Factorization Method HCF by Division Method LCM by Prime Factorization Method LCM by Division Method

## HCF and LCM Formula

Product of Two numbers = (HCF of the two numbers) x (LCM of the two numbers)

## How to find HCF

H.C.F. of Two numbers = Product of Two numbers/L.C.M of two numbers

### How to find LCM

L.C.M of two numbers = Product of Two numbers/H.C.F. of Two numbers

## HCF by Prime Factorization Method

Take an example of finding the highest common factor of 100, 125 and 180.
Now let us write the prime factors of 100, 125 and 180.
100 = 2 × 2 × 5 × 5
125 = 5 × 5 × 5
180 = 3 × 3 × 2 × 2 × 5
The common factors of 100, 125 and 180 are 5
Therefore, HCF (100, 125, 180) = 5

## HCF by Division Method

Steps to find the HCF of any given numbers:

• Larger number/ Smaller Number
• The divisor of the above step / Remainder
• The divisor of step 2 / remainder. Keep doing this step till R = 0(Zero).
• The last step’s divisor will be HCF.

Example:
Let’s take two number 120 and 180
120) 180 (1
120
---------
60) 120 (2
120
---------
000

## LCM by Prime Factorization Method

A technique to find the Least Common Multiple (LCM) of a set of numbers by breaking down each number into its prime factors and then multiplying the highest powers of each prime factor.

Lets take two numbers i.e., 25 and 35, now to calculate the LCM:

• List the prime factors of each number first.
25 = 5 × 5
35 = 7 × 5
• Then multiply each factor the most number of times it occurs in any number.

If the same multiple occurs more than once in both the given numbers, then multiply the factor by the most number of times it occurs.

The occurrence of Numbers in the above example:
5: two times
7: one time
LCM = 7 × 5 × 5 = 175

## LCM by Division Method

Let us see with the same example, which we used to find the LCM using prime factorization.
Solve LCM of (25,35) by division method.
5 | 25, 35
----------
5 | 5, 7
---------
7 | 1, 7
---------
| 1, 1
Therefore, LCM of 25 and 35 = 5  x 5 × 7 = 175

### Questions and Answers of HCF and LCM

Q1: Calculate the highest number that will divide 43, 91 and 183 and leaves the same remainder in each case
(a) 4
(b) 7
(c) 9
(d) 13
Ans:
(a)
Here the trick is
Find the Differences between number
Get the HCF (that differences)
We have here 43, 91 and 183
So differences are
183 – 91 = 92,
183 – 43 = 140,
91 – 43 = 48.
Now, HCF (48, 92 and 140)
48 = 2 × 2 × 2 × 2 × 3
92 = 2 × 2 × 23
140 = 2 × 2 × 5 × 7
HCF = 2 × 2 = 4
And 4 is the required number.

Q2: The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
(a) 25 cm
(b) 15 cm
(c) 35 cm
(d) 55 cm
Ans:
(c)
Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.

Q3: Which of the following is  greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
(a) 9700
(b) 9600
(c) 9800
(d) 9650
Ans:
(b)
Greatest number of 4-digits is 9999.
Now , find the L.C.M. of 15, 25, 40 and 75 i.e.  600.
On dividing 9999 by 600, the remainder is 399.
Hence,  Required number (9999 – 399) = 9600.
Alternatively,
9999/600 = 16.66500
Ignore the decimal points, required number would be 16 * 600 = 9600

The document Important Formula: HCF & LCM | Quantitative Aptitude for SSC CGL is a part of the SSC CGL Course Quantitative Aptitude for SSC CGL.
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## FAQs on Important Formula: HCF & LCM - Quantitative Aptitude for SSC CGL

 1. How do you find the Highest Common Factor (HCF) using the Prime Factorization Method?
Ans. To find the HCF using the Prime Factorization Method, follow these steps: 1. Prime factorize both numbers. 2. Identify the common prime factors between the two numbers. 3. Multiply these common prime factors to find the HCF. For example, let's find the HCF of 24 and 36: - The prime factorization of 24 is 2^3 * 3^1. - The prime factorization of 36 is 2^2 * 3^2. - The common prime factors are 2^2 and 3^1. - Multiplying these common prime factors gives the HCF: 2^2 * 3^1 = 12.
 2. How do you find the Highest Common Factor (HCF) using the Division Method?
Ans. To find the HCF using the Division Method, follow these steps: 1. Divide the larger number by the smaller number. 2. Divide the remainder of the previous step by the divisor. 3. Continue this process until the remainder becomes zero. 4. The last divisor used is the HCF. For example, let's find the HCF of 24 and 36: - Divide 36 by 24, the quotient is 1 and the remainder is 12. - Divide 24 by 12, the quotient is 2 and the remainder is 0. - The last divisor used, 12, is the HCF.
 3. How do you find the Lowest Common Multiple (LCM) using the Prime Factorization Method?
Ans. To find the LCM using the Prime Factorization Method, follow these steps: 1. Prime factorize both numbers. 2. Take the highest power of each prime factor found in either of the numbers. 3. Multiply these prime factors to find the LCM. For example, let's find the LCM of 24 and 36: - The prime factorization of 24 is 2^3 * 3^1. - The prime factorization of 36 is 2^2 * 3^2. - The highest power of 2 is 2^3 and the highest power of 3 is 3^2. - Multiplying these prime factors gives the LCM: 2^3 * 3^2 = 72.
 4. How do you find the Lowest Common Multiple (LCM) using the Division Method?
Ans. To find the LCM using the Division Method, follow these steps: 1. Write the given numbers in a row. 2. Divide the row by the smallest prime number that divides at least one of the numbers. 3. Divide the row by the next smallest prime number that divides at least one of the numbers. 4. Repeat the previous step until each number in the row becomes 1. 5. Multiply all the divisors used in the process to find the LCM. For example, let's find the LCM of 24 and 36: - Start with the numbers 24 and 36. - Divide the row by 2, getting 12 and 18. - Divide the row by 2 again, getting 6 and 9. - Divide the row by 3, getting 2 and 3. - Divide the row by 2, getting 1 and 3. - Divide the row by 3, getting 1 and 1. - The divisors used are 2, 2, 3, and 3. - Multiply these divisors to find the LCM: 2 * 2 * 3 * 3 = 36.
 5. What is the importance of knowing HCF and LCM in mathematics?
Ans. Knowing the HCF and LCM is important in mathematics for various reasons: - HCF helps in simplifying fractions and finding the smallest common denominator. - LCM helps in adding or subtracting fractions with different denominators. - HCF and LCM are used in solving problems related to ratios, proportions, and fractions. - They are also useful in solving problems related to finding the least number of objects that can be arranged in rows or columns. - In algebra, HCF and LCM are used to simplify expressions and solve equations.

## Quantitative Aptitude for SSC CGL

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