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# lcm and hcf

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Intern
Joined: 27 Jun 2013
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27 Jun 2013, 23:33
Find the greatest number of four digits which when divided by 10,11,15 and 22 leaves 3,4,8 and 15 as remainders respectively.

a)9907
b)9903
c)9893
d)None of these

Please provide the solution to the above problem with explanation.
Director
Joined: 24 Aug 2009
Posts: 506
Schools: Harvard, Columbia, Stern, Booth, LSB,
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27 Jun 2013, 23:48
1
KUDOS
Find the greatest number of four digits which when divided by 10,11,15 and 22 leaves 3,4,8 and 15 as remainders respectively.

The best way (as per me) to find the largest number in this case is to directly testing the value rather than finding the LCM n then finding the largest multiple.

a)9907
When divided by 10, it leaves a remainder 7 but we want remainder 3. Thus out
b)9903
When divided by 10, it leaves a remainder 3. ok
When divided by 11, it leaves a remainder 3 but we want remainder 4. Thus out

c)9893
When divided by 10, it leaves a remainder 3. ok
When divided by 11, it leaves a remainder 4. ok
When divided by 15, it leaves a remainder 8. ok
When divided by 22, it leaves a remainder 15. ok

d)None of these
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Re: lcm and hcf   [#permalink] 27 Jun 2013, 23:48
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