Given that the LCM of a and 18 is 36 and the HCF of a and 18 is 2, what is the value of ‘a’?

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To find the value of ‘a’ when the least common multiple (LCM) of ‘a’ and 18 is 36 and the highest common factor (HCF) is 2, we can utilize the relationship between LCM and HCF. The formula that connects these two values is:

LCM(a, b) × HCF(a, b) = a × b

In our case, we can designate ‘b’ as 18:

LCM(a, 18) = 36

HCF(a, 18) = 2

Substituting these values into the formula gives us:

36 × 2 = a × 18

This simplifies to:

72 = a × 18

Next, we can solve for ‘a’:

a = 72 / 18

Calculating this, we find:

a = 4

Now let’s verify our answer: If ‘a’ equals 4, we can check the HCF and the LCM:

  1. Calculating the HCF of 4 and 18, we find that both share the factor 2, thus confirming the HCF is 2.
  2. For the LCM, the multiples of 4 (i.e., 4, 8, 12, 16, 20, 24, 28, 32, 36…) and of 18 (i.e., 18, 36, 54…) show that the first common multiple is indeed 36.

Hence, both the HCF and the LCM conditions are satisfied:

Therefore, the value of ‘a’ is 4.

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