Find the greatest number of five digits which | vedclass

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(D) First,find the $L.C.M.$ of the divisors $4, 6, 10,$ and $15$.Prime factorization: $4 = 2^2, 6 = 2 	imes 3, 10 = 2 	imes 5, 15 = 3 	imes 5$.$L.C

Vedclass · Accepted Answer

$99963$

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(D) First,find the $L.C.M.$ of the divisors $4, 6, 10,$ and $15$.Prime factorization: $4 = 2^2, 6 = 2 	imes 3, 10 = 2 	imes 5, 15 = 3 	imes 5$.$L.C.M. = 2^2 	imes 3 	imes 5 = 4 	imes 3 	imes 5 = 60$.The greatest five-digit number is $99999$.Divide $99999$ by $60$ to find the remainder: $99999 \div 60 = 1666$ with a remainder of $39$.Subtract the remainder from the greatest five-digit number to find the largest number divisible by $60$: $99999 - 39 = 99960$.To leave a remainder of $3$ in each case,add $3$ to this number: $99960 + 3 = 99963$.

Find the greatest number of five digits which when divided by $4, 6, 10$ and $15$ leaves the same remainder $3$ in each case.

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