LCM and HCF
 Four runners started running simultaneously from a point on a circular track. They took 200 seconds, 300 seconds, 360 seconds and 450 seconds to complete one round. After how much time do they meet at the starting point for the first time ?

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Required time = LCM of 200, 300, 360 and 450 seconds
We find , LCM of 200, 300, 360 and 450 seconds = 1800 secondsCorrect Option: A
Required time = LCM of 200, 300, 360 and 450 seconds
We find , LCM of 200, 300, 360 and 450 seconds = 1800 seconds
∴ Required time = 1800 seconds
 Five bells begin to toll together and toll respectively at intervals of 6, 7, 8, 9 and 12 seconds. After how many seconds will they toll together again ?

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Required time = LCM of 6, 7, 8, 9 and 12 seconds = 504 seconds
Correct Option: C
Required time = LCM of 6, 7, 8, 9 and 12 seconds = 504 seconds
 The greatest number of four digits which when divided by 3, 5, 7, 9 leave remainders 1, 3, 5, 7 respectively is :

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The difference between divisor and the corresponding remainder is equal.
LCM of 3, 5, 7 and 9 = 315
Largest 4digit number = 9999
∴ Number divisible by 315 = 9999 – 234 = 9765Correct Option: A
The difference between divisor and the corresponding remainder is equal.
LCM of 3, 5, 7 and 9 = 315
Largest 4digit number = 9999
∴ Number divisible by 315 = 9999 – 234 = 9765
Required number = 9765 – 2 = 9763
 Three bells ring simultaneously at 11a.m. They ring at regular intervals of 20 minutes, 30 minutes, 40 minutes respectively. The time when all the three ring together next is

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LCM of 20, 30 and 40 minutes = 120 minutes
Hence, the bells will toll together again after 2 hours i.e. at 1 p.m.Correct Option: B
LCM of 20, 30 and 40 minutes = 120 minutes
Hence, the bells will toll together again after 2 hours i.e. at 1 p.m.
Required time = 1 p.m.

L.C.M. of 2 , 4 , 5 is 3 9 6

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As we know that ,
LCM of fractions = LCM of numerators HCF of denominators LCM = LCM of 2, 4, 5 HCF of 3, 9, 6 Correct Option: B
As we know that ,
LCM of fractions = LCM of numerators HCF of denominators LCM = LCM of 2, 4, 5 HCF of 3, 9, 6 LCM = 20 3