In step 2 of the 3-step procedure for finding the LCM on p.37 of Math Essentials, it says: "take each prime factor to the highest power". How is "highest power" determined?

For example, in Q.2 on p.38, I identify the prime factors of each of 8, 10 and 12 as:

8: 2 . 2. 2
10: 2 . 5
12: 2 . 2 . 3

We arrive at the answer of 120 by multiplying 8 x 3 x 5. I assume the "highest power" of the prime factor 2 in the above example means 2^3 for the integer 8? (For the integer 12, it would be 2^4. For the integer 32 it would be 2^5).

Is this the correct interpretation?

You are correct (except 16 would be 2^4 12 would be 3 * 2^2)

For the LCM of 8, 10, 12,

we need 2^3 (since 2^3 = 8)

... 5 (since 10 = 5*2)

and .. 3 (since 12 = 3*2*2)

2^3 * 5 * 3 = 120

-- Veritas Help