The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F.?a)8b)12c)24d)35Correct answer is option 'D'. Can you explain this answer?

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The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F.?

a)
8
b)
12
c)
24
d)
35

Correct answer is option 'D'. Can you explain this answer?

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The L.C.M. of three different numbers is 120. Which of the following c...

We know that:
LCM is the least common multiple of the given numbers whereas HCF is the highest common factor of those numbers.
Then, LCM is the multiplication of one common factor of the numbers and the other different factors of the numbers.
Write the LCM = 120 into factored form, that is
120 = 2 × 2 × 2 × 3 × 5
= 4(2 × 3 × 5)
⇒ 4 is the common factor of the numbers.
So, the HCF of three numbers is a multiple of 4.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
Therefore, 35 is not the multiple of 4, then 35 cannot be their HCF.

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