What is LCM of two numbers?

In mathematics, least common multiple which is commonly known as LCM is defined as the smallest non-zero number which is divisible by both given numbers 6 and 20.

Properties of LCM

  • LCM follows associative property, that means LCM(6, 20) = LCM(20, 6).
  • 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 6 and 20 is 60, where 6 and 20 are less than 60.
  • The LCM of two or more prime numbers is their product.

Steps to find lcm of 6 and 20 by Listing Method

Example: Find lcm of 6 and 20 by Listing Method

  • Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120
  • Multiples of 20: 20, 40, 60, 80, 100, 120

Hence, LCM of 6 and 20 is 60.

Steps to find LCM of 6 and 20 by Common Division Method

Example: Find lcm of 6 and 20 by Common Division Method

2 6 20
2 3 10
3 3 5
5 1 5
1 1

Hence, LCM of 6 and 20 is 2 x 2 x 3 x 5 = 60.

Steps to find lcm of 6 and 20 by Formula

Example: Find lcm of 6 and 20 by Formula

  • GCF of 6 and 20 = 2
  • LCM of 6 and 20 = (6 x 20) / 2
  • => 120 / 2

Hence, LCM of 6 and 20 is 60.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 6 and 20 minutes respectively to go round once. Find at what time they will run together?

Franky and Joy are running on a circular track. They take 6 and 20 minutes respectively to go round once. We need to find out at what time (minimum) they will run together again. For this we need to find the LCM of 6 and 20.
So, LCM of 6 and 20 is 60.

A shopkeeper sells candies in packet of 6 and chocolates in packet of 20. 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 6 and 20.
So, LCM of 6 and 20 is 60.

Both the cricket team and the rugby team had games, today. The cricket team plays every 6 days and the basketball team plays every 20 days. When will both teams have games on the same day again?

Given that the cricket team plays every 6 days and the basketball team plays every 20 days, so for finding the next time when both teams will play again we need to find the LCM of 6 and 20.
So, LCM of 6 and 20 is 60.

Freddy saves 6 dollars every day while Nikki saves 20 dollars every day. What is the least number of days it will take each person to save the same amount of money?

To find the least number of days that would be taken to be able to save the same amount of dollars we need to find the LCM of 6 and 20.
So, LCM of 6 and 20 is 60.

Boxes that are 6 inches tall are being pilled next to boxes that are 20 inches tall. What is the least height in feet at which the two piles will be the same height?

To find the least height in feet at which the two piles will be at same height we will find LCM of 6 and 20.
So, LCM of 6 and 20 is 60.

Sammy's company prints 6 textbooks at a time. Daniel's company prints textbooks in sets of 20 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 6 and 20.
So, LCM of 6 and 20 is 60.

Ariel exercises every 6 days and Rubel every 20 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 6 and 20 is 60.