Find the greatest number of four digits which | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) To find the greatest four-digit number divisible by $24, 28, 30$,and $35$,we first calculate the $L.C.M.$ of these numbers.$\begin{array}{r|rrrr}

Vedclass · Accepted Answer

$9240$

Vedclass · Answer

(B) To find the greatest four-digit number divisible by $24, 28, 30$,and $35$,we first calculate the $L.C.M.$ of these numbers.$\begin{array}{r|rrrr} 2 & 24, & 28, & 30, & 35 \ \hline 2 & 12, & 14, & 15, & 35 \ \hline 3 & 6, & 7, & 15, & 35 \ \hline 5 & 2, & 7, & 5, & 35 \ \hline 7 & 2, & 7, & 1, & 7 \ \hline & 2, & 1, & 1, & 1 \end{array}$$L.C.M. = 2 	imes 2 	imes 2 	imes 3 	imes 5 	imes 7 = 840$.The greatest four-digit number is $9999$.Divide $9999$ by $840$:$9999 \div 840 = 11$ with a remainder of $759$.To find the greatest four-digit number divisible by $840$,subtract the remainder from $9999$:$9999 - 759 = 9240$.Thus,the required number is $9240$.

Find the greatest number of four digits which is exactly divisible by $24, 28, 30$ and $35$.

Similar Questions

The product of two numbers is $4107$. If the $HCF$ of these numbers is $37$,then the greater number is

What is the $L.C.M.$ of $25, 30, 35$ and $40$?

The $LCM$ of two numbers is $495$ and their $HCF$ is $5.$ If the sum of the numbers is $100,$ then their difference is

The least multiple of $7,$ which leaves a remainder of $4,$ when divided by $6, 9, 15,$ and $18$ is

The least number, which when divided by $48, 60, 72, 108$ and $140$ leaves $38, 50, 62, 98$ and $130$ as remainders respectively is

Vedclass Test Series

Exam Paper Generator

Online Exam Module