**The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:**

A.30

B.22

C.40

D.60

Answer

Option (c) is correct

**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.

**The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:**

A.534

B.486

C.544

D.548

Answer

Option (d) is correct

**Explanation –**

Required number = (L.C.M. of 12, 15, 20, 54) + 8

= 540 + 8

= 548.

**The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:**

A.124

B.100

C.111

D.175

Answer

Option (c) is correct

**Explanation –**

Let the numbers be 37a and 37b.

Then, 37a x 37b = 4107

ab = 3.

Now, co-primes with product 3 are (1, 3).

So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).

Greater number = 111.

**The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:**

A.1

B.2

C.3

D.5

Answer

Option (b) is correct

**Explanation –**

Let the numbers 13a and 13b.

Then, 13a x 13b = 2028

ab = 12.

Now, the co-primes with product 12 are (1, 12) and (3, 4).

**The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:**

A.10

B.14

C.23

D.30

Answer

Option (c) is correct

**Explanation –**

L.C.M. of 5, 6, 4 and 3 = 60.

On dividing 2497 by 60, the remainder is 37.

Number to be added = (60 – 37) = 23

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