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# LCM & HCF Quiz for SBI PO

IBPS EXAM Guru

1. A fruit vendor has to arrange some number of fruits in rows. When he put five fruits in each row he
was left with one fruit . Then he tried six fruits in a row, then 8 , then 9, then 12. But always he was left
with one fruit . so he thought for a while and put 13 fruits in a row and then he was left with none . what
is the smallest number of fruits ?
1)3601 2)6301 3)2601 4)4601 5)None of these
Solution: (1).when 5 or 6 or 8 or 9 or 12 fruits are arra nged in rows, one fruit is left.
LCM ( 5,6,8,9,12 ) = 360
Then the number of fruits is 360x + 1 .
It is given , number of fruits perfectly divisible by 13

Then (360x + 1) / 13
Substitute x = 1
= (360 x 1 +1 ) / 13
X = 2,3,4 , ………………..
X = 10
(360 x 10 + 1) / 13
is perfectly divisible
= 3601 / 13 = perfectly divisible
Alternately :
Among the options only first option is perfectly divisible by 13

2. What is the LCM of (m+1) (m+5) (m-3)2 and (m-3) (m+1)3 (m+5)2
1).(m+5) (m+1)(m-3)   2).(m+5)2 (m+1)3 (m-3)2
3).(m+5)(m+1)   4).(m+5)2 (m+1) (m-3)
5)None of these
Solution: (2). LCM [ (m+1) (m+5) (m-3)2, (m-3)(m+1)3(m+5)2 ]
Consider all greater powers
Ans = (m+5)2 (m+1)3 (m-3)2

3. If the LCM of A & B is C . Find their HCF.
1) (ABC)2  2) ABC / AB  3) AB / C  4)Cannot be determined  5)none of these
Solution: (3). First Number = A
Second Number = B
Given LCM (A,B) = C
LCM x HCF = A x B

C x HCF = A x B
HCF = AxB / C hence answer is AB / C

4. Find the least number of tiles required to lay the floor of length 150 cm and width 125 cm .
1) 40   2) 20   3) 30   4) 25   5) None of these
Solution: (4).This sum is based on equal distribution then HCF (150,125) = 30

5. Find the greatest number of 5 digits which when divided by 3,5,8,12 have 2 as remainder .
1) 99999  2) 99958  3) 99960  4) 99962  5) None of these
Solution ; (5). LCM (3,,5,8,12) = 120
Then 120x+2 = max.5 digits
When x = 833
Then 120 x 833 +2
99960 + 2