What is LCM of two numbers?

In mathematics, least common multiple which is commonly known as LCM is defined as the smallest non-zero number which is divisible by both given numbers 11 and 15.

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 11 and 15 is 165, where 11 and 15 are less than 165.
  • 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(11, 15) = LCM(15, 11).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 11 and 15 by Listing Method

Example: Find lcm of 11 and 15 by Listing Method

  • Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165
  • Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165

Hence, LCM of 11 and 15 is 165.

Steps to find LCM of 11 and 15 by Common Division Method

Example: Find lcm of 11 and 15 by Common Division Method

3 11 15
5 11 5
11 11 1
1 1

Hence, LCM of 11 and 15 is 3 x 5 x 11 = 165.

Steps to find lcm of 11 and 15 by Formula

Example: Find lcm of 11 and 15 by Formula

  • GCF of 11 and 15 = 1
  • LCM of 11 and 15 = (11 x 15) / 1
  • => 165 / 1

Hence, LCM of 11 and 15 is 165.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 11 and 15 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 11 and 15 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 11 and 15.
So, LCM of 11 and 15 is 165.

Both the cricket team and the rugby team had games, today. The cricket team plays every 11 days and the basketball team plays every 15 days. When will both teams have games on the same day again?

Given that the cricket team plays every 11 days and the basketball team plays every 15 days, so for finding the next time when both teams will play again we need to find the LCM of 11 and 15.
So, LCM of 11 and 15 is 165.

Steve spends 11 dollars every day while George spends 15 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 11 and 15.
So, LCM of 11 and 15 is 165.

Boxes that are 11 inches tall are being pilled next to boxes that are 15 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 11 and 15.
So, LCM of 11 and 15 is 165.

Find the LCM of 11 and 15 using GCF method.

Greatest common factor or gcf of 11 and 15 is GCF(11, 15) x LCM(11, 15) = (11 x 15) / GCF(11, 15) = 165.

Find the least common multiple of 11 and 15.

Least common multiple of 11 and 15 is 165.

Find the least number which is exactly divisible by 11 and 15.

Least number which is exactly divisible by 11 and 15 is 165.