Grades 9-10 Video Solutions 2021-video 2021 9-10/14

video 2021 9-10/14

Video Transcription

Video Summary

The problem asks how many numbers less than 2021 have a remainder of 5 when divided by 6, 7, 8, and 9. By finding the least common multiple (LCM) of these numbers (504), the solution identifies the pattern repeats every 504 numbers. Evaluating around 2021, which is near 504 times 4 (2016), indicates the remainder pattern aligns with the start of each 504 cycle. Thus, there are 4 numbers that satisfy the condition. The answer is 4.

Keywords

remainder

LCM

divisibility

number theory

pattern