What does LCM mean in mathematics?

The least common multiple or LCM of two numbers 18 and 6 is defined as the smallest positive integer which is divisible by both of them. It is represented by LCM(18, 6).

Properties of LCM

  • LCM follows associative property, that means LCM(18, 6) = LCM(6, 18).
  • LCM follows commutative property, which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • LCM follows distributive property, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 18 and 6 is 18, where 18 and 6 are less than 18.
  • The LCM of two or more prime numbers is their product.

Steps to find lcm of 18 and 6 by Listing Method

Example: Find lcm of 18 and 6 by Listing Method

  • Multiples of 18: 18, 36, 54, 72, 90, 108
  • Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108

Hence, LCM of 18 and 6 is 18.

Steps to find LCM of 18 and 6 by Common Division Method

Example: Find lcm of 18 and 6 by Common Division Method

2 18 6
3 9 3
3 3 1
1 1

Hence, LCM of 18 and 6 is 2 x 3 x 3 = 18.

Steps to find lcm of 18 and 6 by Formula

Example: Find lcm of 18 and 6 by Formula

  • GCF of 18 and 6 = 6
  • LCM of 18 and 6 = (18 x 6) / 6
  • => 108 / 6

Hence, LCM of 18 and 6 is 18.

Examples

A shopkeeper sells candies in packet of 18 and chocolates in packet of 6. What is the least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate?

The least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate we need to find the lcm of 18 and 6.
So, LCM of 18 and 6 is 18.

Both the cricket team and the rugby team had games, today. The cricket team plays every 18 days and the basketball team plays every 6 days. When will both teams have games on the same day again?

Given that the cricket team plays every 18 days and the basketball team plays every 6 days, so for finding the next time when both teams will play again we need to find the LCM of 18 and 6.
So, LCM of 18 and 6 is 18.

Steve spends 18 dollars every day while George spends 6 dollars every day. What is the least number of days it will take each person to spend the same amount of money?

To find the least number of days that would be taken to be able to spend the same amount of dollars we need to find the LCM of 18 and 6.
So, LCM of 18 and 6 is 18.

Sammy's company prints 18 textbooks at a time. Daniel's company prints textbooks in sets of 6 at a time. According to a survey done by a committee, both companies printed the same number of textbooks last year. Find the least number of books that each company would have printed.

To find the least number of textbooks that each company could have printed we need to find the LCM of 18 and 6.
So, LCM of 18 and 6 is 18.

Ariel exercises every 18 days and Rubel every 6 days. They both excercised today. How many days will it be until they excercise together again?

The problem can be solved using LCM, because we are trying to figure out the least time until they excercise together again.
So, LCM of 18 and 6 is 18.

Find the least common multiple of 18 and 6.

Least common multiple of 18 and 6 is 18.

Find the least number which is exactly divisible by 18 and 6.

Least number which is exactly divisible by 18 and 6 is 18.