HCF and LCM

Q.

The L.C.M. of 22, 54, 108, 135 and 198 is _____

1. 1980

2. 330

3. 5940

4. 11880

5. None

Q.

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:

1. 1683

2. 2000

3. 2273

4. 1783

5. 1777

Q.

Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is:

1. 50

2. 30

3. 40

4. 60

Q.

Find the two numbers nearest to the $10000$ which are exactly divisible by each $2,3,4,5,6and7$.

Q. A five-digit number is formed using the digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers?(1993)

1. 6666600
2. 6666666
3. None of these
4. 6666660

Q.

Write all the numbers less than $100$ which are common multiples of $3$ and $4$.

Q. The L.C.M. of two numbers is 14560 and their H.C.F. is 13. If one of them is 416, then which of the following is the other number?

1. 380
2. 460
3. 455
4. 450
5. 446

Q. The H.C.F. of two numbers is 24. Which of the following numbers can be their L.C.M.?

1. 75
2. 84
3. 120
4. 128
5. 148

Q.

The least number by which 1470 must be divided to get a number which is a perfect square is?

1. 5

2. 6

3. 15

4. 30

5. 45

Q. The traffic lights at three different road crossings change after 24 seconds, 36 seconds and 54 seconds respectively. If they all change simultaneously at 10:50:00 am, then at what time will they again change simultaneously?

1. None of these
2. 10:18:36 am
3. 10:17:02 am
4. 10:16:54 am
5. 10:22:12 am

Q. The L.C.M. of two numbers is 225 and their H.C.F. is 5. If one of the numbers is 25, the other number will be ____.

1. 625
2. 5
3. 25
4. 45
5. 225

Q. 279936, 46656, 7776, 1296, 216, ?

1. 46
2. 66
3. 36
4. 26
5. 60

Q. The L.C.M. of two numbers is 1920 and their H.C.F. is 16. If one of the numbers is 128, find the other number.

1. 284
2. 204
3. 260
4. 240
5. 320

Q.

The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M. ?

1. 24

2. 48

3. 56

4. 60

5. 64

Q. A is set of positive integers such that when divided by 2, 3, 4, 5, 6 leaves the remainders 1, 2, 3, 4, 5 respectively. How many integers between 0 and 100 belong to set A?

(CAT 1998)

1. 0
2. None of these
3. 1
4. 2

Q.

The greatest number which will divide $4003,4126,$ and $4249:$

1. $43$

2. $4$

3. $2$

4. $3$

5. $1$

Q. The L.C.M. of two numbers is 1820 and their H.C.F. is 26. If one of numbers is 130 then the other number is _____.

1. 70
2. 1264
3. 1690
4. 298
5. 364

Q.

The product of two numbers is $6300$ and their $H.C.F.$ is $15.$ How many pairs of such numbers are there$?$

1. $2$

2. $6$

3. $10$

4. $3$

Q. Three pieces of cakes of weights $4\frac{1}{2}$ lbs, $6\frac{3}{4}$ lbs and $7\frac{1}{5}$ lbs respectively are to be divided into parts of equal weights. Further, each part must be as heavy as possible. If one such part is served to each guest, then what is the maximum number of guests that could be entertained? (CAT 2001)

1. 72
2. 54
3. 20
4. None of these

Q. The H.C.F. and L.C.M. of two numbers are 7 and 140 respectively. If the numbers are between 20 and 45, the sum of the numbers is _____.

1. 29
2. 77
3. 63
4. 56
5. 70

Q.

Two numbers are in the ratio 11:13. If their HCF is 15, what are the numbers?

1. 165, 195

2. 155, 185

3. 145, 175

4. 135, 145

5. 175, 185

Q.

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is :

1. 235

2. 305

3. None

4. 123

5. 127

Q. 179 180 172 199 135 ?

1. 240
2. 256
3. 260
4. 236
5. 272

Q. Choose the most appropriate option to replace (?).
4 200 369 513 634 ?

1. 788
2. 755
3. 715
4. 734
5. None of these

Q. Find the least number which when divided by 15, 21, 24 and 32 leaves the same remainder 2 in each case.

1. 3362
2. 3360
3. 3456
4. 3266
5. 3364

Q.

What is the smallest number which when increased by 5 is divisible by 36, 63 and 108?

1. 753

2. 751

3. 756

4. 754

Q. The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M?

1. 48
2. 24
3. 56
4. 60
5. All of these

Q. Find the unit digit of the LCM of $7^{3001}–1$ and $7^{3001}+1.$

1. 8
2. 9
3. 4
4. 2
5. 6

Q.

36 identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least three chairs and there must be at least three rows. A row is parallel to the front of the room.
How many different arrangements are possible?

1. none

2. 20

3. 21

4. 22

5. 23

Q. 445 444 436 409 343 220

1. 436
2. 343
3. 444
4. 409
5. 220