Hello Friends, Under " HCF and LCM : Types of Questions Asked in Competitive Exams ", we will discuss various varieties of question asked under section HCF and LCM in various competitive exams.

**Type 1 :**Find the HCF of Composite Number

**Qusetion 1 :**Find the HCF of 224, 448 and 550

**Solution :**By Prime Factorisation Method,

224 = 2 x 2 x 2 x 2 x 2 x 7

448 = 2 x 2 x 2 x 2 x 2 x 2 x 7

550 = 2 x 5 x 5 x 11

So, HCF of 224, 448 and 550 is 2

**Type 2 :**Find the LCM of Composite Number

**Question 2 :**Find the LCM of 25, 55 and 75

**Solution :**By Prime Factorisation Method,

25 = 5 x 5

55 = 5 x 11

75 = 3 x 5 x 5

So, LCM of 25, 55 and 75 = 5 x 5 x 11 = 275

**Type 3 :**Find the Least Number which is exactly divisible by given numbers.

**Question 3 :**Find the least number which is exactly divisible by 25, 55 and 75

**Note :**Same question as Type 2 only it is asked in a tricky way

**Type 4 :**Find the HCF and LCM of Fractions and Decimals

**Question 4 :**Find L.C.M. of 1.05 and 2.1

**Solution :**First, take LCM of 105 and 210 i.e 210

Now, write in decimal i.e 2.1 hence, LCM of 1.05 and 2.1 is 2.10

**Type 5 :**Find the numbers if their HCF and ratio are given.

**Question 5 :**H.C.F. of two numbers is 11. If these two numbers are in the ratio of 12 : 11, then find the numbers.

**Solution :**The required two numbers are 12 x 11 = 132 and 11 x 11 =121

**Type 6 :**Find the other number if one number and their HCF and LCM is given

**Question 6 :**The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then find the other number

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

So, 275 x Y = 11 x 7700

=> Y = 308

**Type 7 :**Find the least number, which when divided by another number leaves a remainder

**Question 7 :**Find the least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8

**Solution :**Required number = (L.C.M. of 12, 15, 20, 54) + 8

= 540 + 8 = 548

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