Last Updated on May 4, 2023
What is the lowest positive integer that is divisible by…
Solution:
We need to determine the smallest number that is divisible by the following:
1, 2, 3, 4, 5, 6, and 7
That is, we need to find the least common multiple of 1, 2, 3, 4, 5, 6, and 7; however, it may be easiest to use the answer choices and the divisibility rules.
Let’s start with answer choice A, 420.
Since 420 is an even number we know 2 divides into 420.
Since the digits of 420 add to 6 (a multiple of 3), we know 3 divides into 420.
Since the last two digits of 420 (20) is divisible by 4, we know 4 divides into 420.
Since 420 ends in a zero, we know 5 divides into 420.
Since 420 is divisible by both 2 and 3, we know 6 divides into 420.
Finally, we need to determine whether 420 is divisible by 7. While there is no easy divisibility rule for 7, we do know that 7 divides evenly into 42, so it must also divide evenly into 420.
Thus, we have determined that 420 is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive.
Answer: A
