6.
The least multiple of 7, which leaves a remainder of 4. when divided by 6, 9, 15 and 18 is:
• A.
74
• C.
184
• B.
94
• D.
364
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Explanation :

L.C.M. of 6, 9, 15 and 18 is 90.

Let required number be 90k + 4, which is a multiple of 7.

Least value of k for which (90k + 4) is divisible by 7 is k = 4

 Required number  = 90 x 4 + 4 = 364

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7.
L.C.M. of two prime numbers x and y (x > y) is 161 The value of 3yx is:
• A.
-2
• C.
1
• B.
-1
• D.
2
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Explanation :

H.C.F. of two prime numbers is 1. Product of numbers = (1 x 161) = 161

Let the numbers be a and b. Then, ab = 161.

Now, co-primes with product 161 are (1, 161) and (7, 23).

Since x and y are prime numbers and x > y, we have x = 23 and y = 7.

 3y – x = (3 x 7) - 23 = -2

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8.
The L.C.M. of two numbers is 48. The numbers are in the ratio 2:3. the sum of the numbers is:
• A.
28
• C.
40
• B.
32
• D.
64
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Explanation :
 Let the numbers be 2x and 3x. Then, their L.C.M. = 6x. So, 6x = 48 or x = 8 The numbers are 16 and 24. Hence, required sum = (16 + 24) = 40
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9.
The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
• A.
1677
• C.
2523
• B.
1683
• D.
3363
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Explanation :

L.C.M. of 5, 6, 7, 8 = 840.

 Required number is of the form 840k + 3.

Least value of k for which (840k + 3) is divisible by 9 is k = 2.

 Required number = (840 x 2 + 3) = 1683

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10.
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
• A.
276
• C.
322
• B.
299
• D.
345