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 27 and 9

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 27 and 9 is 27, where 27 and 9 are less than 27.
  • 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(27, 9) = LCM(9, 27).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 27 and 9 by Listing Method

Example: Find lcm of 27 and 9 by Listing Method

  • Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243
  • 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

Hence, LCM of 27 and 9 is 27.

Steps to find LCM of 27 and 9 by Common Division Method

Example: Find lcm of 27 and 9 by Common Division Method

3 27 9
3 9 3
3 3 1
1 1

Hence, LCM of 27 and 9 is 3 x 3 x 3 = 27.

Steps to find lcm of 27 and 9 by Formula

Example: Find lcm of 27 and 9 by Formula

  • GCF of 27 and 9 = 9
  • LCM of 27 and 9 = (27 x 9) / 9
  • => 243 / 9

Hence, LCM of 27 and 9 is 27.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 27 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 27 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 27 and 9.
So, LCM of 27 and 9 is 27.

Both the cricket team and the rugby team had games, today. The cricket team plays every 27 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 27 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 27 and 9.
So, LCM of 27 and 9 is 27.

Steve spends 27 dollars every day while George spends 9 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 27 and 9.
So, LCM of 27 and 9 is 27.

Boxes that are 27 inches tall are being pilled next to boxes that are 9 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 27 and 9.
So, LCM of 27 and 9 is 27.

Find the LCM of 27 and 9 using GCF method.

Greatest common factor or gcf of 27 and 9 is GCF(27, 9) x LCM(27, 9) = (27 x 9) / GCF(27, 9) = 27.

Find the least common multiple of 27 and 9.

Least common multiple of 27 and 9 is 27.

Find the least number which is exactly divisible by 27 and 9.

Least number which is exactly divisible by 27 and 9 is 27.