Problem Solving (PS) | Re: The product of all the prime numbers less than 20 is closest

SOLUTION

The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?

(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5

We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.

# of different approximations are possible.

Approach #1:

2*5=10;
3*7=~20 (actually more than 20);
11*19=~200 (actually more than 200);
13*17=~200 (actually more than200);

\(2*3*5*7*11*13*17*19\approx{10*20*200*200=8*10^6}\approx{10^7}\) .

Answer:C.

Approach #2: