The least number, which when divided by 48, 6 | vedclass

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

Question

(B) First, observe the difference between each divisor and its corresponding remainder:$48 - 38 = 10$$60 - 50 = 10$$72 - 62 = 10$$108 - 98 = 10$$140 -

Vedclass · Accepted Answer

$15110$

Vedclass · Answer

(B) First, observe the difference between each divisor and its corresponding remainder:$48 - 38 = 10$$60 - 50 = 10$$72 - 62 = 10$$108 - 98 = 10$$140 - 130 = 10$Since the difference is constant $(10)$, the required number is $(LCM 	ext{ of } 48, 60, 72, 108, 140) - 10$.Prime factorization:$48 = 2^4 	imes 3$$60 = 2^2 	imes 3 	imes 5$$72 = 2^3 	imes 3^2$$108 = 2^2 	imes 3^3$$140 = 2^2 	imes 5 	imes 7$$LCM = 2^4 	imes 3^3 	imes 5 	imes 7 = 16 	imes 27 	imes 35 = 15120$.Therefore, the required number $= 15120 - 10 = 15110$.

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

Similar Questions

The $LCM$ of two numbers is $1008$ and their $HCF$ is $36$. If one of the two numbers is $144$,find the other number.

Find the greatest number which will divide $2112$ and $2792$ leaving the remainder $4$ in each case.

Find the largest number of four digits exactly divisible by $14, 24, 27$ and $32$.

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

The $LCM$ of two prime numbers $x$ and $y$ $(x > y)$ is $161$. Find the value of $(3y - x)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module