Question

The LCM of two numbers is 12 times their HCF.The sum of HCF and LCM is 403.If one number is 93.Find the other

Answer 1

Answer:

Step-by-step explanation:

Let the HCF be x

LCM = 12x

x + 12x = 403

13x = 403

x = 403/13 = 31

HCF = 31

LCM = 372

HCF * LCM = Product of two numbers.

Let the other number be y

31*372 = 93*y

y = (31*372)/93

y = 31*4 = 124.

Answer 2

$\huge\rm\underline\blue{GIVEN:}$

• $\large\rm{LCM\:of\:two\:Numbers\:=\:12(HCF)}$
• $\large\rm{HCF+LCM\:=\:403}$
• $\large\rm{One\:of\:the\:number\:=\:93}$

$\huge\rm\underline\blue{TO\:FIND:}$

• $\large\rm{Other\:Number}$

$\huge\rm\underline\blue{SOLUTION:}$

$\large\rm{Let\: HCF\rightarrow'x'}$

$\large\rm{Let \:LCM\rightarrow'y'}$

$\large\rm{\implies{x+y\:=\:403}}$

$\large\rm{\implies{y\:=\:403-x----eq(1)}}$

$\large\rm{y\:=\:12x---eq(2)}$

$\large\rm{In\:both\:equations\:LHS\:is\:equal\:so\:RHS\:can\:be\:equated}$

$\large\rm{\implies{12x=\:403-x}}$

$\large\rm{\implies{13x\:=\:403}}$

$\large\rm{\implies{x\:=\:\frac{403}{13}}}$

$\large\rm{\implies{x\:=\:31}}$

$\large\rm{From\:eq(1)\:y\:=\:403-31}$

$\large\rm{\implies{y\:=\:372}}$

$\large\rm{\therefore{HCF\:=\:31}}$

$\large\rm{LCM\:=\:372}$

$\large\rm{Let\:the\:other\:Number\:be\:'a'}$

$\large\rm\bold{\boxed{Product\:of\:two\:numbers\:=\:LCM(HCF)}}$

$\large\rm{\implies{a(93)\:=\:(372)(31)}}$

$\large\rm{\implies{a\:=\:\frac{(372)(31)}{93}}}$

$\large\rm{\implies{a\:=\:124}}$

$\large\rm{\therefore{The\:other\:Number\:=\:124}}$