The least multiple of 7, which leaves a remai | vedclass

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

Question

(D) First,find the $LCM$ of $6, 9, 15,$ and $18$.$\begin{array}{c|cccc} 2 & 6, & 9, & 15, & 18 \ \hline 3 & 3, & 9, & 15, & 9 \ \hline 3 & 1, & 3, &

Vedclass · Accepted Answer

$364$

Vedclass · Answer

(D) First,find the $LCM$ of $6, 9, 15,$ and $18$.$\begin{array}{c|cccc} 2 & 6, & 9, & 15, & 18 \ \hline 3 & 3, & 9, & 15, & 9 \ \hline 3 & 1, & 3, & 5, & 3 \ \hline & 1, & 1, & 5, & 1 \end{array}$$LCM = 2 	imes 3 	imes 3 	imes 5 = 90$.Let the number be of the form $90k + 4$,where $k$ is a positive integer.We are given that the number is divisible by $7$. Therefore,$90k + 4 \equiv 0 \pmod{7}$.Simplifying $90 \pmod{7}$: $90 = 7 	imes 12 + 6$,so $90 \equiv 6 \equiv -1 \pmod{7}$.Thus,$-k + 4 \equiv 0 \pmod{7}$,which means $k \equiv 4 \pmod{7}$.The least positive integer $k$ is $4$.Substituting $k = 4$ into the expression $90k + 4$:Required number $= 90(4) + 4 = 360 + 4 = 364$.

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

Similar Questions

The $HCF$ of two numbers is $8$. Which one of the following can never be their $LCM$?

The $LCM$ of two numbers is $48$. The numbers are in the ratio $2:3$. Find the sum of the numbers.

$A$ number, when divided successively by $4, 5$ and $6$, leaves remainders $2, 3$ and $4$ respectively. The least such number is

Let $N$ be the greatest number that will divide $1305, 4665,$ and $6905,$ leaving the same remainder in each case. Then the sum of the digits in $N$ is:

Find the greatest number of five digits which when divided by $8, 9$ and $10$ leaves $3$ as a remainder in each case.

Vedclass Test Series

Exam Paper Generator

Online Exam Module