How do we define LCM?

LCM, abbreviation for least common multiple, is defined as the smallest number that is the product of two or more numbers 32 and 9

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 32 and 9 is 288, where 32 and 9 are less than 288.
  • LCM is associative which means LCM(32, 9) = LCM(9, 32).
  • 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 or more prime numbers is their product.

Steps to find lcm of 32 and 9 by Listing Method

Example: Find lcm of 32 and 9 by Listing Method

  • Multiples of 32: 32, 64, 96, 128, 160, 192, 224, 256, 288
  • Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288

Hence, LCM of 32 and 9 is 288.

Steps to find LCM of 32 and 9 by Common Division Method

Example: Find lcm of 32 and 9 by Common Division Method

2 32 9
2 16 9
2 8 9
2 4 9
2 2 9
3 1 9
3 1 3
1 1

Hence, LCM of 32 and 9 is 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288.

Steps to find lcm of 32 and 9 by Formula

Example: Find lcm of 32 and 9 by Formula

  • GCF of 32 and 9 = 1
  • LCM of 32 and 9 = (32 x 9) / 1
  • => 288 / 1

Hence, LCM of 32 and 9 is 288.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 32 and 9 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 32 and 9 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 32 and 9.
So, LCM of 32 and 9 is 288.

A shopkeeper sells candies in packet of 32 and chocolates in packet of 9. 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 32 and 9.
So, LCM of 32 and 9 is 288.

Both the cricket team and the rugby team had games, today. The cricket team plays every 32 days and the basketball team plays every 9 days. When will both teams have games on the same day again?

Given that the cricket team plays every 32 days and the basketball team plays every 9 days, so for finding the next time when both teams will play again we need to find the LCM of 32 and 9.
So, LCM of 32 and 9 is 288.

Sammy's company prints 32 textbooks at a time. Daniel's company prints textbooks in sets of 9 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 32 and 9.
So, LCM of 32 and 9 is 288.

Ariel exercises every 32 days and Rubel every 9 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 32 and 9 is 288.

What is the relation between LCM and GCF( Greatest Common Factor)?

Greatest common factors or gcf of 32 and 9 is GCF(32, 9) * LCM(32, 9) = (32 x 9) / GCF(32, 9) = 288.

Find the least number which is exactly divisible by 32 and 9.

Least number which is exactly divisible by 32 and 9 is 288.