# Lowest common multiple (LCM)

**What is LCM?**

The least common multiple, lowest common multiple (LCM), or smallest common multiple is the “smallest positive number that is a multiple of two or more numbers”. LCM of two integers a and b, usually denoted by LCM(a, b).

In other words LCM(x, y) is “the smallest positive integer that is divisible by both x and y”.

**What is a “Multiple” ?**

A multiple of a number is the product of that number and any other whole number. We get multiple of a number when we multiply it by another number. Such as multiplying number by 1, 2, 3, 4, 5, etc, but not zero. It is like the multiplication table.

Some examples of multiples:

Multiples of 3 are: 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,…

Multiples of 7 are: 7,14,21,28,35,42,49,56,63,…

**What is a “Common Multiple” ?**

Common multiples of 3 and 7 are simply the numbers that are in both lists:

21,42 and 63 are the first few common multiples of the numbers 3 and 7.

Therefore least common multiple LCM(3,7) is 21.

**What of kind of problems can be solved by LCM?**

Problem: One chocolate van visits Jhon’s shop every 3 days and another choclate van visits his shop every 7 days in winter season. If both vans visited today, when is the next time both vans will visit on the same day on his shop?

Van Days of Visits

1st – 3,6,9,12,15,18,21,24,27,30,33,36,39,42,…

2nd – 7,14,21,28,35,42,…

Solution: Both chocolate vans will visit Jhon’s shop in 21 days and in 42 days. However, the problem says: when is the next time both vans will visit on the same day?, so the final answer is “In 21 Days”.