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

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

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The LCM of 6, 12 and 18 = 36 = 6^{2}
Correct Option: D
The LCM of 6, 12 and 18 = 36 = 6^{2} = 36
Hence , required answer is 36.
 The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35, is

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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 35Correct 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
 The smallest number, which when increased by 5 is divisible by each of 24,32, 36 and 564, is

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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 = 864Correct 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
 The greatest 4digit number exactly divisible by 10, 15, 20 is

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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 4digit number = 9999Correct 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 4digit number = 9999
∴ Required number = 9999 – remainder = 9999 – 39 = 9960