General Mathematics

Question: The L.C.M. of two numbers is 45 times their H.C.F. If one of the numbers is 125 and the sum of H.C.F. and L.C.M. is 1150, the other number is :
A
215

B
220

C
225

D
235

Note: solution: Let H.C.F. be h and L.C.M. be l. Then, `l=45h` `and l+h=1150`. `:. 45h+h =1150` `or h=25`. `So, l=(1150-25)=1125`. `:.`other number =`(25 xx 1125)/125 ` `=225`.
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Question: The product of two 2-digit numbers is 2028 and their G.C.M. is 13. The numbers are:
A
26,78

B
39,52

C
13,156

D
36,68

Note: solution: Let the numbers be 13a and 13b.Then, `13a xx 13b = 2028` `=> ab = 12`. Now, co-primes with product 12 are `(1,12) and (3,4)`. So, the numbers with H.C.F. 13 and product 2028 are: `(13 xx 1, 13 xx 12) and (13 xx 3, 13 xx 4)`. `:.` Required 2-digit numbers are `39 & 52`.
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Question: About the number of pairs which have 16 as their H.C.F. and 139 as their L.C.M., we can definitely say that :
A
only one such pair exists

B
only two such pairs exist

C
many such pairs exist

D
no such pair exists

Note: solution: H.C.M. of two numbers divides their L.C.M. exactly. Since 16 is not a factor of 136, it follows that there does not exist any pair of numbers with H.C.F. 16 and L.C.M. 136.
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Question: The L.C.M. of three different numbers is 120. Which of the following can not be their H.C.F. ?
A
8

B
12

C
24

D
36

Note: solution: Since H.C.F. is always a factor of L.C.M., so we can not have three numbers with H.C.F. 35 and L.C.M. 120.
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Question: The H.C.F. and L.C.M. of two numbers are 50 and 250 respectively. If the first number is divided by 2, the quotient is 50. The second number is:
A
50

B
100

C
125

D
250

Note: solution: First number =(50`xx`2) = 100. Second number =`((50xx250)/100)` = 125.
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Question: The product of two numbers is 1320 and their H.C.F. is 6. The L.C.M. of the numbers is :
A
7920

B
220

C
1314

D
1326

Note: solution: L.C.M. = `((Product of numbers)/(Their H.C.M.))` = `1320/6` =220.
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Question: The greatest number which exactly divides 105, 1001 & 2436 is :
A
3

B
7

C
11

D
21

Note: solution: H.C.F. of 2436 & 1001 is 7. Also, H.C.F of 105 & 7 is 7. `:.` H.C.F. of 105, 1001 & 2436 is 7.
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Question: The largest number which divides 25, 73 and 97 to leave the same remainder in case is ease is :
A
24

B
23

C
21

D
6

Note: solution: Required number =H.C.F. of `(73 -25),(97-73) & (97-25)` =H.C.F. of `48, 24 & 72 = 24`.
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Question: The greatest number that will divide 187, 233 and 279 leaving the same remainder in each case is :
A
30

B
36

C
46

D
56

Note: solution: Required number = H.C.F. of (233-187),(279-233) & (279-187) = H.C.F. of 46,46 & 92 =46.
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Question: The greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case, is :
A
64

B
124

C
156

D
260

Note: solution: Required number =H.C.F. of (1356-12),(1860-12) & (2764-12) =H.C.F. of 1344, 1856 & 2752 = 64.
1. Report

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Question: The L.C.M. of two numbers is 45 times their H.C.F. If one of the numbers is 125 and the sum of H.C.F. and L.C.M. is 1150, the other number is :

Question: The product of two 2-digit numbers is 2028 and their G.C.M. is 13. The numbers are:

Question: About the number of pairs which have 16 as their H.C.F. and 139 as their L.C.M., we can definitely say that :

Question: The L.C.M. of three different numbers is 120. Which of the following can not be their H.C.F. ?

Question: The H.C.F. and L.C.M. of two numbers are 50 and 250 respectively. If the first number is divided by 2, the quotient is 50. The second number is:

Question: The product of two numbers is 1320 and their H.C.F. is 6. The L.C.M. of the numbers is :

Question: The greatest number which exactly divides 105, 1001 & 2436 is :

Question: The largest number which divides 25, 73 and 97 to leave the same remainder in case is ease is :

Question: The greatest number that will divide 187, 233 and 279 leaving the same remainder in each case is :

Question: The greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case, is :