Find the smallest natural number that is divisible by the first 12 natural numbers.
A) 27,720
B) 27,730
C) 27,719
D) 27,715
E) 27,726

Question

Find the smallest natural number that is divisible by the first 12 natural numbers. ​
A) 27,720
B) 27,730
C) 27,719
D) 27,715
E) 27,726

Quizplus · Accepted Answer

To find the smallest natural number that is divisible by the first 12 natural numbers, we need to find the least common multiple (LCM) of the numbers 1 through 12.

Prime factorizing each of the numbers:

1 = 1
2 = 2
3 = 3
4 = 2 x 2
5 = 5
6 = 2 x 3
7 = 7
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
11 = 11
12 = 2 x 2 x 3

Taking the highest power of each prime factor:

2^3 x 3^2 x 5 x 7 x 11 = 27720

Therefore, the smallest natural number that is divisible by the first 12 natural numbers is 27,720.

Find the Smallest Natural Number That Is Divisible by the First