26.
The L.C.M. of 22, 54, 108, 135 and 198 is:
• A.
330
• C.
5940
• B.
1980
• D.
11880
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Explanation :

 2 22 - 54 - 108 - 135 - 198 3 11 - 27 - 54 - 135 - 99 3 11 - 9 - 18 - 45 - 33 3 11 - 3 - 6 - 15 - 11 11 11 - 1 - 2 - 5 - 11 1 - 1 - 2 - 5 - 1

L.C.M. = 2 x 3 x 3 x 3 x 11 x 2 x 5 = 5940

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27.
 The smallest fraction, which each of 6 , 5 , 10 will divide exactly, is : 7 14 21
•  A. 30 7
•  C. 60 147
•  B. 30 98
•  D. 50 294
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Explanation :

 Required fraction = L.C.M. of 6 , 5 , 10 = L.C.M. of 6, 5, 10 = 30 7 14 21 H.C.F. of 7, 14, 21 7

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28.
The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is:
• A.
4
• C.
8
• B.
6
• D.
12
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Explanation :

 Let the required numbers be 33a and 33b. Then, 33a + 33b = 528 a + b = 16

Now, co-primes with sum 16 are (1, 15), (3, 13), (5, 11) and (7, 9).

 Required numbers are (33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)

The number of such pairs is 4

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29.
The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F.?
• A.
8
• C.
24
• B.
12
• D.
35
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Explanation :
 Since H.C.F. is always a factor of L.C.M., we cannot have three numbers with H.C.F. 35 and L.C.M. 120
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30.
H.C.F. of 4 x 27 x 3125, 8 x 9 x 25 x 7 & 16 x 81 x 5 x 11 x 49 is:
• A.
180
• C.
540
• B.
360
• D.
1260