What does LCM mean in mathematics?

The least common multiple or LCM of two numbers 13 and 8 is defined as the smallest positive integer which is divisible by both of them. It is represented by LCM(13, 8).

Properties of LCM

  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(13, 8) = LCM(8, 13).
  • LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
  • The LCM of two given numbers is always greater than the given numbers numbers. Eg- LCM of 13 and 8 is 104, where 104 is greater than 13 and 8.

Steps to find lcm of 13 and 8 by Listing Method

Example: Find lcm of 13 and 8 by Listing Method

  • Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104
  • Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104

Hence, LCM of 13 and 8 is 104.

Steps to find LCM of 13 and 8 by Common Division Method

Example: Find lcm of 13 and 8 by Common Division Method

2 13 8
2 13 4
2 13 2
13 13 1
1 1

Hence, LCM of 13 and 8 is 2 x 2 x 2 x 13 = 104.

Steps to find lcm of 13 and 8 by Formula

Example: Find lcm of 13 and 8 by Formula

  • GCF of 13 and 8 = 1
  • LCM of 13 and 8 = (13 x 8) / 1
  • => 104 / 1

Hence, LCM of 13 and 8 is 104.

Examples

Steve spends 13 dollars every day while George spends 8 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 13 and 8.
So, LCM of 13 and 8 is 104.

Boxes that are 13 inches tall are being pilled next to boxes that are 8 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 13 and 8.
So, LCM of 13 and 8 is 104.

Sammy's company prints 13 textbooks at a time. Daniel's company prints textbooks in sets of 8 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 13 and 8.
So, LCM of 13 and 8 is 104.

Ram and Deepika are running on a circular track. They start at the same time. They take 13 and 8 minutes respectively to go round once. Find at what time they will run together?

Ram and Deepika are running on a circular track. They take 13 and 8 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 13 and 8.
So, LCM of 13 and 8 is 104.

Find the LCM of 13 and 8 using GCF method.

Greatest common factor or gcf of 13 and 8 is GCF(13, 8) x LCM(13, 8) = (13 x 8) / GCF(13, 8) = 104.

Find the least common multiple of 13 and 8.

Least common multiple of 13 and 8 is 104.

Find the least number which is exactly divisible by 13 and 8.

Least number which is exactly divisible by 13 and 8 is 104.