# What is LCM of 15 and 18?

LCM of 15 and 18 is 90

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 15 and 18 By Listing Method 3.   Steps to find LCM of 15 and 18 By Common Division Method 4.   Steps to find LCM of 15 and 18 By Formula 5.   Examples

#### Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 15 and 18, is defined as the smallest positive integer that is divisible by both. It is written as LCM(15, 18).

#### Properties of LCM

• The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 15 and 18 is 90, where 15 and 18 are less than 90.
• 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(15, 18) = LCM(18, 15).
• LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

### Example: Find lcm of 15 and 18 by Listing Method

• Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270
• Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270

Hence, LCM of 15 and 18 is 90.

### Example: Find lcm of 15 and 18 by Common Division Method

 2 15 18 3 15 9 3 5 3 5 5 1 1 1

Hence, LCM of 15 and 18 is 2 x 3 x 3 x 5 = 90.

### Example: Find lcm of 15 and 18 by Formula

• GCF of 15 and 18 = 3
• LCM of 15 and 18 = (15 x 18) / 3
• => 270 / 3

Hence, LCM of 15 and 18 is 90.

#### Examples

Franky and Joy are running on a circular track. They start at the same time. They take 15 and 18 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 15 and 18 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 15 and 18.
So, LCM of 15 and 18 is 90.

Boxes that are 15 inches tall are being pilled next to boxes that are 18 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 15 and 18.
So, LCM of 15 and 18 is 90.

Sammy's company prints 15 textbooks at a time. Daniel's company prints textbooks in sets of 18 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 15 and 18.
So, LCM of 15 and 18 is 90.

Ariel exercises every 15 days and Rubel every 18 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 15 and 18 is 90.

Find the LCM of 15 and 18 using GCF method.

Greatest common factor or gcf of 15 and 18 is GCF(15, 18) x LCM(15, 18) = (15 x 18) / GCF(15, 18) = 90.

Find the least common multiple of 15 and 18.

Least common multiple of 15 and 18 is 90.

Find the least number which is exactly divisible by 15 and 18.

Least number which is exactly divisible by 15 and 18 is 90.