Question

The hcf and lcm of a pair of numbers are 11 and 1001 respectively. find the smaller of the two numbers given that their sum is 220.

Answer 1

given hcf = 11

         lcm = 1001

formula to find their product is

   H C F x LCM   = product of the two numbers

      11   x  1001   =  11011

so, the factors of 11011 :-

1573 x 7, 11 x 1001, 143 x 77...

So from this the product of the two numbers be = 143 and 77

from this the smaller number is 77

Answer 2

Answer:

Step-by-step explanation:

Let the two  numbers be X and Y

given

HCF=11

LCM=1001

as HCF is comman factor, so 11 multiple of X and Y

these two numbers are 11X and 11Y

we know that,

Product of two numbers= LCM*HCF

so,  11X*11Y=11*1001

X*Y=91      ----(1)

Sum is given as 220.

11X+11Y=220

X+Y=20    ----(2)

Solving equations (1) and (2), we get

X=13 and Y= 7

required numbers 11*X=11*13=143

                               11*Y=11*7=77

smaller number is 77.

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