SSC conducts CGL exam once every year for recruiting the Grade-‘B’ & ‘C’ officers in various government offices and ministries. Quantitative Aptitude is one subject with the other three. HCF & LCM is one of the most important topics asked in the aptitude section, as there will be 1-2 questions based on this.

In addition to this, the exam prep team of jagranjosh has come up with concept & sample questions for HCF and LCM. The concept described in the following text will help you to understand the all types of questions. The sample questions framed in this article are prepared by keeping the pattern & difficulty level of the question paper.

**SSC CGL Aptitude preparation tips: HCF & LCM**

In the ongoing text, you will find the all types of questions based on HCF & LCM with their solution methods. Let us go through all of these-

**Factors and Multiples**

Factors and multiples are different things. However, they both involve multiplication. If a number divides another number exactly without leaving any remainder, then the divider number is called a factor of the dividend number. Whereas multiples are, what we get after multiplying the number by an integer.

In another words, we can say that if x divides y exactly without leaving any remainder, then x is a factor of y and y is a multiple of x.

**SSC Quantitative Aptitude tricks: Simple & Compound Interest**

**For Example- **

- 8 exactly divides 16, then 8 is a factor of 16 and 16 is a multiple of 8.
- 2 is a factor of 4 and 4 is a multiple of 2.
- 3 is a factor of 6 and 6 is a multiple of 3.
- 6 is a factor of 12 and 12 is a multiple of 6 etc.

**Common Factors**

A common factor of two or more numbers is that number, which divides each of them exactly.

E.g. 3 is a common factor of 9 and 12 because 3 divides both 9 and 12 exactly. Similarly, 2 is a common factor of 4, 6 and 8.

**Common Multiple**

A common multiple of two or more numbers is a number, which is completely divisible (without leaving remainder) by each of them.

e.g., 30 is a common multiple of 2, 3, 5, 6, 10, and 15 because 30 are exactly divisible by each of 2, 3, 5, 6, 10, and 15.) Similarly, 36 is a common multiple of 2, 3, 4, 6, 9, 12, and 18.

**SSC Quantitative Aptitude tricks: Algebraic formulae & their applications**

**LCM (Least Common Multiple): - **The LCM of two or more given numbers is the least number to be exactly divisible by each of them.

For instance, we can obtain LCM of 4 and 12 as follows-

The multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36,…

The multiples of 12 = 12, 24, 36, 48, 60, 72, ...

Now, common multiple of 4 and 12 = 12, 24, 36, ...

Hence, the LCM of 4 and 12 = 12

**A few points to Remember**

- Number1 * Number2 = HCF (Number1, Number2) * LCM (Number1, Number2).
- The greatest number, which divides the numbers x, y and z … leaving remainders a, b and c, respectively, will be = HCF[ (x – a), (y – b), (z – c)]

**Note** This formula is true for any range of numbers.

**SSC Quantitative Aptitude Tips and Tricks: Partnership**

- The greatest number that will divide x, y and z ... leaving the same remainder in each case, will be = HCF [|x – y|, |y – z| |z – x|…].
- The least number, which when divided by x, y and z leaves the same remainder k in each case, is given by [LCM of (x, y, z) + k].

**Note** This formula is true for any range of numbers.

- The greatest number, which when divided by x, y and z leaves the remainders a, b and c respectively, is given by [LCM of (x, y, z)] - k.

If k = (x -a) = (y - b) = (z -c);

**Note** This formula is true for any number of numbers.

**SSC Quantitative Aptitude tips & tricks: Boats & Streams**

- When the HCF of each pair of n given numbers is a and their LCM is b, then the product of these numbers is given by (a)
^{n – 1}X b or (HCF)^{n – 1}LCM. - All the fractions must be in their lowest terms. If they are not in their lowest terms, then conversion in the lowest form is required before finding LCM and HCF.
- If two numbers are primes to each other (i.e., co-primes), then their HCF should be equal to 1. Conversely, if their HCF is equal to 1, the numbers are prime to each other.
- In questions related to ringing of bells, LCM is calculated for different time sequences.

For more preparation tips and tricks for Quantitative Aptitude section, keep on visiting the SSC webpage.

**All the Best!**