The LCM of two number is 336 and HCF is 2 if one of the number is 14 find the other number

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The HCF of two numbers is 28 and their LCM is 336 . If one of the number is 112 . What is the other number?

Solution

HCF * LCM = product of two numbers. HCF of two numbers is 28 Their LCM is 336 If one of the number is 112 The other will be

(336*28)/112 = 84

Concept:

Product of two numbers = L.C.M. × H.C.F.

Calculation:

We have, 

L.C.M. × H.C.F. = 336

Let the two numbers be a and b, a > b.

⇒ ab = 336      ----(1)

Also, a - b = 10

⇒ a = 10 + b

On substituting this value in equation (1), we get

(10 + b)b = 336

⇒ b2 + 10b - 336 = 0

⇒ (b + 24)(b - 14) = 0

⇒ b = -24 or 14

Neglecting the negative value, we get

b = 14

∴ a = 10 + 14 = 24

Hence, the two numbers are 14 and 24.

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