Question

The difference of L.C.M. and H.C.F. of the numbers 40, 240 and 480 is equal to twice a number. Find the number.

Answer 1

Answer:

number = 100

Step-by-step explanation:

LCM(40,240,80) = 240

HCF(40,240,80) = 40

Difference = 240-40=200

given 200 is equal to twice a number.

let 200 = 2x

100 = x

Answer 2

The value of the number is 220.

Given:

The difference between L.C.M. and H.C.F. of the numbers 40, 240, and 480 is equal to twice a number

To Find:

The value of the number.

Solution:

At first, we are required to find the H.C.M and L.C.M of 40, 240, and 480.

40 = 2×2×2×5

240 = 2×2×2×2×3×5

480 = 2×2×2×2×2×3×5

L.C.M = 2×2×2×2×2×3×5

          = 480

H.C.F = 2×2×2×5

          = 40

Therefore, The L.C.M is 480 and the H.C.F is 40 for the numbers 40, 240, and 480.

From the given data, Let x be the number then

L.C.M - H.C.F = 2x   ---------(1)

Substitute the value of L.C.M and H.C.F in the equation(1)

480 - 40 = 2x

2x = 440

x = 220

Therefore, The value of the number is 220.

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