LCM

The least common multiple, or LCM, is the smallest number that is a common multiple shared by two or more numbers. It helps determine the earliest point at which two different recurring schedules or intervals will match.

Multiples of a number

When an action repeats at a regular interval, the counts produce a sequence known as multiples. Visiting a house once every two days means arriving on dates that are multiples of two. These numbers begin with 2, 4, and 6, and continue through 8, 10, 12, 14, 16, 18, and 20. An event that occurs once every five days instead follows multiples of five, producing values such as 5, 10, 15, and 20.

Common multiples

• Each number produces an ongoing list of multiples that keeps going.
• Common multiples are the values that appear in the multiple lists of both numbers.
• Comparing the multiples of two with the multiples of five reveals values that belong to both.
• The numbers 10 and 20 are common multiples because they appear in both lists.

Identifying the least common multiple

• The least common multiple, or LCM, is the smallest number among the shared common multiples.
• The list of common multiples for two and five starts with 10 and 20 and continues onward.
• The smallest number among these shared values is 10.
• Therefore, 10 is the least common multiple of 2 and 5.

Example from the lesson

Rakesh wants to meet his friend Dhanraj, but Dhanraj is away in the village. Dhanraj only comes home once every five days, meaning his visits occur on multiples of five. Rakesh visits every two days, coming on November 2nd, November 4th, and November 6th, which are multiples of two. To figure out the first date they will meet, Rakesh finds the least common multiple of 2 and 5. The smallest common multiple is 10, so Rakesh knows Dhanraj will definitely be home if he visits on November 10th.