LCM and divisibility?

Question

Find
(a)the greatest number of 4 digits such that they are exactly divisible by 12 , 15 , 20 and 35


Ans : LCM of 12,15,20 and 35 = 420

420)9999(23  

        9660

        -------

        339

required number =9999-339 = 9663

Question : i object this answer given in my book . this 9663 is not divisible by 420 finally......... which was our primary requirement !!!!

try dividing 9663 by 420 :-( ..this does not divide ..wondering......how this could be the answer !

do you think the book is wrong ?

---------------------
hurrah , thank you.
the book had printing mistake ! you are right .....i did not see that

Thank you

Answer 1

there is a mistake in last statement

9999-339 = 9660 and not 9663

Answer 2

LCM=420

the greatest 4 digit number divisible by given numbers is 9660

(when you divide 9999 by 420 you will get 23 times of 420 which gives 9660)

required number =9999-339 = 9660

the unit digit in the subtraction operation in your book is wrong , it must be 0

Answer 3

Required number = 9999-339= 9660
and this is divisible by 420
if the answer is 9663 then this is a misprint

Answer 4

books often have typos, even in a teacher edition. from my perspective, however, it seems that you understand quite clearly how to find lcm of two or more terms together, and i really wouldn't worry too much abour my answer matching that of the book =)