LCM and HCF
 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 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 LCM fo two prime numbers p and q, (p > q) is 161. The value of (3q – p) :

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LCM of p and q = 161
∴ pq = 23 × 7
∴ p = 23; q = 7
∴ 3q – p = 3 × 7 – 23Correct Option: A
LCM of p and q = 161
∴ pq = 23 × 7
∴ p = 23; q = 7
∴ 3q – p = 3 × 7 – 23
The value of (3q – p) = 21 – 23 = – 2
 The LCM of four consecutive numbers is 60. The sum of the first two numbers is equal to the fourth number. What is the sum of four numbers?

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We find LCM of 60 ,
∴ 60 = 2 × 2 × 3 × 5
i.e., Numbers = 2, 3, 4 and 5Correct Option: B
We find LCM of 60 ,
∴ 60 = 2 × 2 × 3 × 5
i.e., Numbers = 2, 3, 4 and 5
∴ Required sum = 2 + 3 + 4 + 5 = 14
 Three bells ring at intervals of 36 seconds, 40 seconds and 48 seconds respectively. They start ringing together at a particular time. They will ring together after every

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Required answer = LCM of 36, 40 and 48 seconds
∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720Correct Option: B
Required answer = LCM of 36, 40 and 48 seconds
= 720 secondsRequired answer = 720 minutes = 12 minutes 60
∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720