What does LCM mean in mathematics?

The least common multiple or LCM of two numbers 23 and 7 is defined as the smallest positive integer which is divisible by both of them. It is represented by LCM(23, 7).

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 23 and 7 is 161, where 23 and 7 are less than 161.
  • 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, 7) = LCM(7, 23).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 23 and 7 by Listing Method

Example: Find lcm of 23 and 7 by Listing Method

  • Multiples of 23: 23, 46, 69, 92, 115, 138, 161
  • Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161

Hence, LCM of 23 and 7 is 161.

Steps to find LCM of 23 and 7 by Common Division Method

Example: Find lcm of 23 and 7 by Common Division Method

7 23 7
23 23 1
1 1

Hence, LCM of 23 and 7 is 7 x 23 = 161.

Steps to find lcm of 23 and 7 by Formula

Example: Find lcm of 23 and 7 by Formula

  • GCF of 23 and 7 = 1
  • LCM of 23 and 7 = (23 x 7) / 1
  • => 161 / 1

Hence, LCM of 23 and 7 is 161.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 23 and 7 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 7 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 7.
So, LCM of 23 and 7 is 161.

Boxes that are 23 inches tall are being pilled next to boxes that are 7 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 7.
So, LCM of 23 and 7 is 161.

Sammy's company prints 23 textbooks at a time. Daniel's company prints textbooks in sets of 7 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 7.
So, LCM of 23 and 7 is 161.

Ariel exercises every 23 days and Rubel every 7 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 7 is 161.

Find the LCM of 23 and 7 using GCF method.

Greatest common factor or gcf of 23 and 7 is GCF(23, 7) x LCM(23, 7) = (23 x 7) / GCF(23, 7) = 161.

Find the least common multiple of 23 and 7.

Least common multiple of 23 and 7 is 161.

Find the least number which is exactly divisible by 23 and 7.

Least number which is exactly divisible by 23 and 7 is 161.