LCM and HCF
 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
 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
 Three electronic devices make a beep after every 48 seconds, 72 seconds and 108 seconds respectively. They beeped together at 10 a.m. The time when they will next make a beep together at the earliest is

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Required time = LCM of 48, 72 and 108 seconds
∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432 seconds = 7 minutes 12 secondCorrect Option: A
Required time = LCM of 48, 72 and 108 seconds
∴ LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432 seconds = 7 minutes 12 second
∴ Required time = 10 a.m. + 7 minutes 12 second = 10 : 07 : 12 hours
 Three tankers contain 403 litres, 434 litres, 465 litres of diesel respectively. Then the maximum capacity of a container that can measure the diesel of the three containers exact number of times is

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Greatest capacity of measuring vessel
= HCF of 403 litres, 434 litres and 465 litres
First of all we find HCF of 403 and 434
Again , HCF of 31 and 465Correct Option: A
Greatest capacity of measuring vessel
= HCF of 403 litres, 434 litres and 465 litres
First of all we find HCF of 403 and 434
Again , HCF of 31 and 465
∴ Greatest capacity of measuring vessel = 31 litres
 The greatest number that will divide 729 and 901 leaving remainders 9 and 5 respectively, is

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We know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of (729 – 9) = 720 and (901 – 5) = 896
H.C.F = 16Correct Option: B
We know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of (729 – 9) = 720 and (901 – 5) = 896
H.C.F = 16
Hence , required answer = 16.