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.