Track / Stage 3 / 259 of 260 #259 of 1964

Problem 259

AMC 10/12, early questions

Number theory Difficulty 4.0 Find the answer South African Mathematics Olympiad · South Africa

The smallest number bigger than $2015$ that is divisible by all of $2$ , $3$ , $4$ , $5$ and $6$ is

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

$2040$

In order to be divisible by $2$ , $3$ , $4$ , $5$ and $6$ , the number only needs to be divisible by $2^2 \times 3 \times 5$ , i.e. it must be a multiple of $60$ . The smallest multiple of $60$ bigger than $2015$ is $2040$ .

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.