HCF & LCM, General Mathematics

Question: The L.C.M. of 26,56,104 and 182 is :
A
546

B
1274

C
728

D
784

Note: solution: 13 | 26 - 56 - 104 - 182 ___|__________________________ 7 | 2 -56 - 8 - 14 ___|___________________________ 2 | 2 - 8 - 8 - 2 ___|___________________________ 4 | 1 - 4 - 4 - 1 ___|___________________________ | 1 - 1 - 1 - 1 `:.`L.C.M.=(13`xx`7`xx`2`xx`4`xx`)=728.
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Question: The L.C.M. of 148 and 185 is :
A
680

B
740

C
3700

D
2960

Note: solution: H.C.F. of 148 and 185 is 37. L.C.M.=`((148xx185)/37)` =740.
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Question: The L.C.M. of `2^3``xx``3^2``xx`5`xx`11, `2^4``xx``3^4``xx``5^2``xx`7 and `2^5``xx``3^3``xx``5^3``xx``7^2``xx`11 is:
A
`2^5``xx``3^4``xx``5^3`

B
`2^5``xx``3^4``xx``5^3``xx``7^3``xx`11

C
`2^3``xx``3^2``xx`5`xx`7`xx`11

D
`2^3``xx``3^2``xx`5

Note: solution: L.C.M. =product of highest powers of prime factors =`2^5``xx``3^4``xx``5^3``xx``7^2``xx`11.
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Question: The L.C.M. of `1/3`,`5/6`,`2/9`,`4/27` is:
A
`1/54`

B
`10/27`

C
`20/3`

D
None of these

Note: solution: L.C.M.=`(L.C.M. of 1,5,2,4)/(H.C.F. of 3,6,9,27)` =`20/3`.
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Question: The L.C.M. of `2/3`,`3/5`,`4/7``9/131` is:
A
36

B
`1/36`

C
`1/1365`

D
`12/455`

Note: solution: L.C.M.=`(L.C.M. of 2,3,4,9)/(H.C.F. of 3,5,7,13)`= `36/1`=36.
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Question: Two numbers are in the ratio of 15 : 11. If their H.C.F. is 13, then the numbers are :
A
12,55

B
105, 77

C
15, 11

D
195,143

Note: solution: Let the required numbers be 15x and 11x. Then ,their H.C.F. is x. so, x=13. `:.`The numbers are 15 `xx` 13 & 11 `xx` 13 i.e. 195 & 143.
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Question: Three numbers are in the ratio 1:2:3 and their H.C.F. is 12. The numbers are:
A
12,24,36

B
10,20,30

C
5,10,15

D
4,8,12

Note: solution: Let the required numbers be x, 2x and 3x. Then, their H.C.F. =x. So, x=12. `:.` The number are 12,24 and 36.
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Question: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are:
A
27,189

B
154,162

C
108,108

D
81,189

Note: solution: Let the required numbers be`27a and 27b`. Then, `27a+27b=216` `=> a+b=8`. Now,co-primes with sum 8 are `(1,7) & (3,5)`. `:.` Required number are `(27 xx 1, 27 xx 7) & (27 xx 3, 27 xx 5)` i.e. `(27,189) & (81,135)`. Out of these, the given one in the answer is the pair `(27,189)`.
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Question: The sum of two numbers is 528 and their H.C.F. is 33. The number of pairs of such numbers satisfying the above condition is:
A
6

B
12

C
8

D
4

Note: solution: Let the required numbers be `33a and 33b`. Then, `33a +33b=528` or `a+b=16.` Now, two co-primes with sum 16 are: `(1,15),(3,13),(5,11) & (7,9)` `:.` Numbers with sum 528 and H.C.F. 33 are: `(33 xx 1, 33 xx 15),(33 xx 3, 33 xx 13),(33 xx 5, 33 xx 11),(33 xx 7, 33 xx 9)`. The number of such pairs is 4.
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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: The L.C.M. of 26,56,104 and 182 is :

Question: The L.C.M. of 148 and 185 is :

Question: The L.C.M. of `2^3``xx``3^2``xx`5`xx`11, `2^4``xx``3^4``xx``5^2``xx`7 and `2^5``xx``3^3``xx``5^3``xx``7^2``xx`11 is:

Question: The L.C.M. of `1/3`,`5/6`,`2/9`,`4/27` is:

Question: The L.C.M. of `2/3`,`3/5`,`4/7``9/131` is:

Question: Two numbers are in the ratio of 15 : 11. If their H.C.F. is 13, then the numbers are :

Question: Three numbers are in the ratio 1:2:3 and their H.C.F. is 12. The numbers are:

Question: The sum of two numbers is 216 and their H.C.F. is 27. The numbers are:

Question: The sum of two numbers is 528 and their H.C.F. is 33. The number of pairs of such numbers satisfying the above condition is:

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