Question

The H.C.F. and L.C.M. of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1 : 4, then the larger of the two numbers is :

• A. 12
• B. 48
• C. 84
• D. 108
• E. 256

Answer 1

The correct option is C

84

Let the numbers be x and 4x.
According to question,

Product of two number is sum of its L.C.M and H.C.F

$x\times 4x=84\times 21$

$4x^2=84\times 21$

$x^2=\frac{84\times 21}{4}$

$x^2=21\times 21$

x = 21

Hence, larger number = 4x = 84.