Find the greatest number of five digits which | vedclass

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(D) First, observe the difference between the divisors and their respective remainders:$12 - 5 = 7$$15 - 8 = 7$$21 - 14 = 7$$25 - 18 = 7$$28 - 21 = 7$

Vedclass · Accepted Answer

$98693$

Vedclass · Answer

(D) First, observe the difference between the divisors and their respective remainders:$12 - 5 = 7$$15 - 8 = 7$$21 - 14 = 7$$25 - 18 = 7$$28 - 21 = 7$Since the difference is constant $(7)$, the required number is $(L.C.M. 	ext{ of } 12, 15, 21, 25, 28) 	imes k - 7$.Calculate the $L.C.M.$ of $12, 15, 21, 25, 28$:$12 = 2^2 	imes 3$$15 = 3 	imes 5$$21 = 3 	imes 7$$25 = 5^2$$28 = 2^2 	imes 7$$L.C.M. = 2^2 	imes 3 	imes 5^2 	imes 7 = 4 	imes 3 	imes 25 	imes 7 = 2100$.The greatest five-digit number is $99999$.Divide $99999$ by $2100$:$99999 \div 2100 = 47$ with a remainder of $1299$.Subtract the remainder from $99999$ to find the largest multiple of $2100$ less than $100000$:$99999 - 1299 = 98700$.Finally, subtract the constant difference $(7)$: $98700 - 7 = 98693$.

Find the greatest number of five digits which when divided by $12, 15, 21, 25$ and $28$ leaves $5, 8, 14, 18$ and $21$ as remainders, respectively.

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