## LCM and HCF

#### LCM and HCF

1. What is the greatest number that divides 263, 935 and 1383 leaving a remainder of 7 in each case ?
1. 30
2. 31
3. 32
4. 35

1. The required greatest number is the HCF of 263-7, 935-7, 1383-7

##### Correct Option: C

The required greatest number is the HCF of 263-7, 935-7, 1383-7
i.e. 256, 928 and 1376 HCF = 32

1. If (x+2) is the HCF of x2 + ax + b and x2 + cx + d , then which one of the following is correct ?
1. a + c = b + d
2. 2a + b = 2c + d
3. b + 2c = 2a + d
4. b - 2c = 2a - d

1. If (x+2) is the HCF of x2 + ax + b and x2 + cx + d.
Then, (-2)2 -2a +b = (-2)2 -2c + d

##### Correct Option: C

If (x+2) is the HCF of x2 + ax + b and x2 + cx + d.
Then, (-2)2 -2a +b = (-2)2 -2c + d
b + 2c = 2a + d

1. Find the greatest possible length which can be used to measure 4m 3cm, 4m 34cm and 4m 65cm exactly.
1. 31 cm
2. 29 cm
3. 28 cm
4. 32 cm

1. Required measure = HCF of 403, 434 and 465

##### Correct Option: A

Required measure = HCF of 403, 434 and 465
= 31 cm

1. Which of the following fractions is the greatest of all ? 7/8, 6/7, 4/5, 5/6 ?
1. 6/7
2. 4/5
3. 5/6
4. 7/8

1. 7 / 8 = 0.875,
6 / 7 = 0.857,
4 / 5 = 0.8 and 5/6 = 0.833
Now, 0.875 > 0.857 > 0.833 > 0.8
So, 7/8 is the greatest

##### Correct Option: D

7 / 8 = 0.875,
6 / 7 = 0.857,
4 / 5 = 0.8 and 5/6 = 0.833
Now, 0.875 > 0.857 > 0.833 > 0.8
So, 7/8 is the greatest

1. L.C.M of 2/3, 4/9, 5/6 and 7/12 is ?
1. 1/18
2. 1/36
3. 35/9
4. 140/3

1. L.C.M = ( L.C.M . of 2, 4, 5, 7) / (H.C.F. of 3, 9, 6, 12)

##### Correct Option: D

L.C.M = ( L.C.M . of 2, 4, 5, 7) / (H.C.F. of 3, 9, 6, 12)
= 140/3