Explanation:
I see what you're trying to do, but there's a mistake in your approach. You are finding the least common multiple (LCM) and highest common factor (HCF) of the numerators and denominators separately, which is not how it works for fractions.
To find the LCM of fractions, you should find the LCM of the denominators and then adjust the numerators accordingly. Let's correct the calculation:
The fractions are: 2/3, 4/9, 5/6, 7/12.
First, find the LCM of the denominators: LCM(3, 9, 6, 12) = 36.
Now, adjust the numerators accordingly:
(2/3) x (12/12) = 24/36
(4/9) x (4/4) = 16/36
(5/6) x (6/6) = 30/36
(7/12) x (3/3) = 21/36
Now, you have:
24/36, 16/36, 30/36, 21/36.
Next, find the LCM of these fractions. The LCM of the numerators is 1 (since they all have a common factor of 1), and the LCM of the denominators is 36.
So, the LCM of 2/3, 4/9, 5/6, 7/12 is:
(1/36) x 36 = 1.
The LCM of these fractions is 1, not 140/3.