The H.C.F. and L.C.M. of two numbers are 12 a | vedclass

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

Question

(C) Let the two numbers be $12x$ and $12y$,where $x$ and $y$ are coprime (i.e.,their $H.C.F.$ is $1$).The $L.C.M.$ of these two numbers is given by $1

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) Let the two numbers be $12x$ and $12y$,where $x$ and $y$ are coprime (i.e.,their $H.C.F.$ is $1$).The $L.C.M.$ of these two numbers is given by $12xy$.According to the problem,$12xy = 924$.Dividing both sides by $12$,we get $xy = \frac{924}{12} = 77$.Now,we need to find pairs of coprime factors $(x, y)$ such that their product is $77$.The factors of $77$ are $1, 7, 11, 77$.The possible pairs $(x, y)$ are $(1, 77)$ and $(7, 11)$.Since both pairs consist of coprime numbers,there are $2$ such pairs.

The $H.C.F.$ and $L.C.M.$ of two numbers are $12$ and $924,$ respectively. Then the number of such pairs is

Similar Questions

The $H.C.F.$ of two numbers is $11$ and their $L.C.M.$ is $693$. If one of the numbers is $77$,find the other.

The greatest number that divides $43, 91,$ and $183$ so as to leave the same remainder in each case is:

Find the greatest number which exactly divides $200$ and $320$.

If the sum of two numbers is $55$ and the $HCF$ and $LCM$ of these numbers are $5$ and $120$ respectively,then the sum of the reciprocals of the numbers is equal to

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module