Question

The sum of L.C.M. and H.C.F. of two numbers is 1260. If their L.C.M. is 900 more than their H.C.F., find the product of two numbers.

• A. $203400$
• B. $194400$
• C. $198400$
• D. $205400$

Answer 1

The correct option is B $194400$

Let the HCF be x

$LCM=HCF+900$

$LCM=x+900$ --(1)

And

$LCM+HCF=1260$

$LCM+x=1260$ --(2)

From (1) and (2)

$(x+900)+x=1260$

$2x+900=1260$

$2x=1260-900$

$2x=360$

$x=\frac{360}{2}$

$x=180$

HCF $=180$

And, from (1),

$LCM=HCF+900$

$LCM=180+900$

$LCM=1080$

By formula, product of the numbers is equal to the product of their HCF and LCM.

Product of numbers $=HCF\times LCM$

$=180\times 1080$

Product $=194400$