LCM and HCF

LCM and HCF

1. The number nearest to 43582 divisible by each of 25, 50 and 75 is :

1. LCM of 25, 50 and 75 = 150
On dividing 43582 by 150, remainder = 82

∴ Required number = 43582 + (150 – 82)

Correct Option: B

LCM of 25, 50 and 75 = 150
On dividing 43582 by 150, remainder = 82

∴ Required number = 43582 + (150 – 82) = 43650

1. The smallest perfect square divisible by each of 6, 12 and 18 is

1. The LCM of 6, 12 and 18 = 36 = 62

Correct Option: D

The LCM of 6, 12 and 18 = 36 = 62 = 36
Hence , required answer is 36.

1. The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35, is

1. We find LCM of 20, 28, 32 and 35

∴ LCM = 2 × 2 × 5 × 7 × 8 = 1120
∴ Required number = 5834 – LCM of 20, 28, 32 and 35

Correct Option: B

We find LCM of 20, 28, 32 and 35

∴ LCM = 2 × 2 × 5 × 7 × 8 = 1120
∴ Required number = 5834 – LCM of 20, 28, 32 and 35
∴ Required number = 5834 – 1120 = 4714

1. The smallest number, which when increased by 5 is divisible by each of 24,32, 36 and 564, is

1. Required number = (LCM of 24, 32, 36 and 54) – 5
Now,LCM of 24, 32, 36 and 54

LCM = 2 × 2 × 2 × 3 × 3 × 3 × 4 = 864

Correct Option: B

Required number = (LCM of 24, 32, 36 and 54) – 5
Now,LCM of 24, 32, 36 and 54

LCM = 2 × 2 × 2 × 3 × 3 × 3 × 4 = 864
∴ Required number = 864 – 5 = 859

1. The greatest 4-digit number exactly divisible by 10, 15, 20 is

1. We know that Greatest n digit number which when divided by three numbers p,q,r leaves no remainder will be Required Number = (n – digit greatest number) – R , R is the remainder obtained on dividing greatest n digit number by L.C.M of p.q,r.
LCM of 10, 15 and 20 = 60
Largest 4-digit number = 9999

Correct Option: B

We know that Greatest n digit number which when divided by three numbers p,q,r leaves no remainder will be Required Number = (n – digit greatest number) – R , R is the remainder obtained on dividing greatest n digit number by L.C.M of p.q,r.
LCM of 10, 15 and 20 = 60
Largest 4-digit number = 9999

∴ Required number = 9999 – remainder = 9999 – 39 = 9960