# H.C.F and L.C.M Aptitude Test Paper 5

21) The LCM of two prime number x and y is 161. If x>y, find the value of 15y-7x.

1. -32
2. -56
3. 38
4. 74

Explanation:

Note: The HCF of two prime numbers = 1

LCM/HCF =161/1 =161
161=7 * 23
The ratio of numbers: 7: 23
Hence, the expression gives15 * 7 - 7 * 23 = -56

22) Find the smallest digit that will leave same remainder 4 in each case when divided by 12, 15, 20, and 54.

1. 454
2. 540
3. 544
4. 450

Explanation:

Take LCM of 12, 15, 20, and 54. It will be = 540.

ATQ, the remainder in each case = 4.

Hence, the required number = 540+4 = 544.

23) What is the number nearest to 10000 which is exactly divisible by 3, 4, 5, 6, 7, and 8?

1. 9956
2. 10080
3. 10096
4. 9240

Explanation:

Take LCM of 3, 4, 5, 6, 7, and 8. It will be = 840.

Now, 10000/840 = 760 (remainder).

840 - 760 = 80. If we add 80 in the given number, the number is exactly divisible by 840.

So, the required number is 10080.

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