GCF AND LCM PRACTICE QUESTIONS FOR SCAT EXAMS INTERMEDIATE LEVEL

Question 1 :

What is the greatest number that divides 720 and 810 without leaving any remainder.

Solution :

From the given question we understand that we are going to find number and it must divides both 720 and 810 without remainder.

HCF  =  5 ⋅ 2 ⋅ 3 ⋅ 3  =  90

Hence 90 is the required greatest number which divides 720 and 810 without remainder.

Question 2 :

Find the greatest number that divides 665, 798 and 931 leaving 5, 6 and 7 respectively. 

Solution :

We know that,

Dividend  =  Divisor x quotient + Remainder

665 - 5  =  660

798 - 6  =  792

931 - 7  =  924

GCF of 660, 792 and 924 is 132. Thus 132 is the greatest number which divides 665, 798 and 931 leaving the remainders 5, 6 and 7.

Question 3 :

The biggest possible square stamps are used to cover a page of an album that is 35 cm long and 28 cm wide. How big is each stamp and how many such stamps are used ?

Solution :

To find biggest possible square stamps, we have to common value length and breadth.

GCF (28, 35) is 7.

So each square stamp will have the side length 7 cm.

Number of square stamps  =  Area of page / area of square stamp

Area of page  =  35 x 28

Area of square stamp  =  7²

Number of square stamps  =  (35 x 28)/7²

  =  5 x 4

  =  20 

Question 4 :

Which is the greatest 6 digit number that is exactly divisible by 4 and 6 ?

Solution :

The greatest 6 digit number  =  999999

The least common multiple of 4 and 6 is 12.

  =  999999 / 12

Quotient  =  83333 and remainder  =  3

999999 - 3  =  999996

Hence the greatest 6 digit number that is exactly divisible by 4 and 6 is 999996.

Question 5 :

Which is the smallest 5 digit number that is exactly divisible by 390 as well as 468 ?

Solution :

LCM of 390 and 468

LCM  =  2 x 3 x 13 x 5 x 6  =  2340

The smallest 5 digit number  =  10000  

Quotient  =  4 and remainder  =  640

The product of 4 and 2340 will be 9360, but it is a four digit number. To find 5 digit number, we have to multiply 5 and 2340.

5 (2340)  =  11700

Hence the smallest 5 digit number which is divisible by 390 and 468 is 11700.

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