What does LCM mean in mathematics?

The least common multiple or LCM of two numbers 23 and 16 is defined as the smallest positive integer which is divisible by both of them. It is represented by LCM(23, 16).

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 23 and 16 is 368, where 23 and 16 are less than 368.
  • LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(23, 16) = LCM(16, 23).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 23 and 16 by Listing Method

Example: Find lcm of 23 and 16 by Listing Method

  • Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, 230, 253, 276, 299, 322, 345, 368
  • Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320, 336, 352, 368

Hence, LCM of 23 and 16 is 368.

Steps to find LCM of 23 and 16 by Common Division Method

Example: Find lcm of 23 and 16 by Common Division Method

2 23 16
2 23 8
2 23 4
2 23 2
23 23 1
1 1

Hence, LCM of 23 and 16 is 2 x 2 x 2 x 2 x 23 = 368.

Steps to find lcm of 23 and 16 by Formula

Example: Find lcm of 23 and 16 by Formula

  • GCF of 23 and 16 = 1
  • LCM of 23 and 16 = (23 x 16) / 1
  • => 368 / 1

Hence, LCM of 23 and 16 is 368.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 23 and 16 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 23 and 16 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 23 and 16.
So, LCM of 23 and 16 is 368.

Boxes that are 23 inches tall are being pilled next to boxes that are 16 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 23 and 16.
So, LCM of 23 and 16 is 368.

Sammy's company prints 23 textbooks at a time. Daniel's company prints textbooks in sets of 16 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 23 and 16.
So, LCM of 23 and 16 is 368.

Ariel exercises every 23 days and Rubel every 16 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 23 and 16 is 368.

Find the LCM of 23 and 16 using GCF method.

Greatest common factor or gcf of 23 and 16 is GCF(23, 16) x LCM(23, 16) = (23 x 16) / GCF(23, 16) = 368.

Find the least common multiple of 23 and 16.

Least common multiple of 23 and 16 is 368.

Find the least number which is exactly divisible by 23 and 16.

Least number which is exactly divisible by 23 and 16 is 368.