Two distinct primes, each greater than 20, are multiplied. What is the least possible product of these two primes?
The first two distinct primes greater than 20 are 23 and 29. Therefore, the least possible product is $23\cdot29=\boxed{667}$.
667
Level 2
Prealgebra
Problem: Two distinct primes, each greater than 20, are multiplied. What is the least possible product of these two primes?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the least possible product of two distinct primes greater than 20, we first identify the smallest primes greater than 20. The first few primes in this range are 23, 29, 31, 37, and so on. 

Next, we need to consider the combinations of these primes to find their products. The smallest two distinct primes are 23 and 29. We calculate their product:

23 * 29 = 667.

We should also check the next smallest pair of distinct primes, which would be 23 and 31:

23 * 31 = 713.

Then we check 29 and 31:

29 * 31 = 899.

Continuing this process with larger primes will yield even larger products. Since 667 is the product of the smallest two distinct primes greater than 20, we conclude that no smaller product can be formed with any other combination of distinct primes in this range.

Thus, the least possible product of two distinct primes, each greater than 20, is confirmed to be 667.<|END_OF_LATENT|> The final answer is $667$.