Question 27

L.C.M of two numbers is 120 and their H.C.F. is 10. Which of the following can be the sum of those two numbers ?

Solution

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L.C.M. = 120 and H.C.F. = 10

Let the numbers be $$10a , 10b$$     (where a,b are co prime)

=> $$10a \times 10b = 120 \times 10$$

=> $$a \times b = 12$$

Since a,b are co primes, the only possibility is $$a = 3 , b = 4$$     (or vice-versa)

=> Numbers = 30 and 40

$$\therefore$$ Sum = 30 + 40 = 70

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