1981 AMC 12 Problem 7

Attempt Problem 7 of the 1981 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1981 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

How many of the first one hundred positive integers are divisible by all of the numbers

2,

3,

4,

5?

0

1

2

3

4

Find the least common multiple of

2,

3,

4,

and

5

Count the multiples of that least common multiple through

100

The least common multiple is

\operatorname{lcm}(2,3,4,5)=60.

Among the positive integers through

100,

only

60

is a multiple of

60.

Thus the count is

1.

Therefore, the correct answer is B.

Problem 7 in other years