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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                        View Hint View Answer Discuss in Forum 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: BWe 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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                        View Hint View Answer Discuss in Forum The LCM of 6, 12 and 18 = 36 = 62 Correct Option: DThe LCM of 6, 12 and 18 = 36 = 62 = 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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                        View Hint View Answer Discuss in Forum LCM of p and q = 161 
 ∴ pq = 23 × 7
 ∴ p = 23; q = 7
 ∴ 3q – p = 3 × 7 – 23Correct Option: ALCM 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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                        View Hint View Answer Discuss in Forum We find LCM of 60 ,  
 ∴ 60 = 2 × 2 × 3 × 5
 i.e., Numbers = 2, 3, 4 and 5Correct Option: BWe 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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                        View Hint View Answer Discuss in Forum Required answer = LCM of 36, 40 and 48 seconds  
 ∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720Correct Option: BRequired 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
 
	