Question

1. Find the greatest 4-digit number which
when divided by 7, 10, 15, 21 and 28 leaves no reminder​

Answer 1

Let the greatest 4-digit number be “N”.

So, N is divisible by 7, 10, 15, 21 and 28.

=>N=K×LCM(7,10,15,21,28)  

Note: K is any natural number such that K* LCM gives us a 4-digit number.

=>N=K×420  

=>N = 420K  

Now the greatest 4-digit number is 9999.

R[9999420]=339  

=>(9999−339)=9660  is divisible by  420  

=>9660=420×23  

=>K=23  

Thus, the greatest 4-digit multiple of 420 is  9660  which is our required number.

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Answer 2

Answer:

9999

Step-by-step explanation:

Let the greatest 4-digit number be “N”.

So, N is divisible by 7, 10, 15, 21 and 28.

=>N=K×LCM(7,10,15,21,28)

Note: K is any natural number such that K* LCM gives us a 4-digit number.

=>N=K×420

=>N = 420K

Now the greatest 4-digit number is 9999.

R[9999420]=339

=>(9999−339)=9660 is divisible by 420

=>9660=420×23

=>K=23