# What is LCM of 13 and 17?

LCM of 13 and 17 is 221

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 13 and 17 By Listing Method 3.   Steps to find LCM of 13 and 17 By Common Division Method 4.   Steps to find LCM of 13 and 17 By Formula 5.   Examples

#### What does LCM mean in mathematics?

The least common multiple or LCM of two numbers 13 and 17 is defined as the smallest positive integer which is divisible by both of them. It is represented by LCM(13, 17).

#### Properties of LCM

• The LCM of two or more prime numbers is exactly equal to their product.
• LCM is associative which means LCM(13, 17) = LCM(17, 13).
• 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 given numbers is always greater than the given numbers numbers. Eg- LCM of 13 and 17 is 221, where 221 is greater than 13 and 17.

### Example: Find lcm of 13 and 17 by Listing Method

• Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221
• Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221

Hence, LCM of 13 and 17 is 221.

### Example: Find lcm of 13 and 17 by Common Division Method

 13 13 17 17 1 17 1 1

Hence, LCM of 13 and 17 is 13 x 17 = 221.

### Example: Find lcm of 13 and 17 by Formula

• GCF of 13 and 17 = 1
• LCM of 13 and 17 = (13 x 17) / 1
• => 221 / 1

Hence, LCM of 13 and 17 is 221.

#### Examples

Steve spends 13 dollars every day while George spends 17 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 13 and 17.
So, LCM of 13 and 17 is 221.

Boxes that are 13 inches tall are being pilled next to boxes that are 17 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 13 and 17.
So, LCM of 13 and 17 is 221.

Sammy's company prints 13 textbooks at a time. Daniel's company prints textbooks in sets of 17 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 13 and 17.
So, LCM of 13 and 17 is 221.

Ram and Deepika are running on a circular track. They start at the same time. They take 13 and 17 minutes respectively to go round once. Find at what time they will run together?

Ram and Deepika are running on a circular track. They take 13 and 17 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 13 and 17.
So, LCM of 13 and 17 is 221.

Find the LCM of 13 and 17 using GCF method.

Greatest common factor or gcf of 13 and 17 is GCF(13, 17) x LCM(13, 17) = (13 x 17) / GCF(13, 17) = 221.

Find the least common multiple of 13 and 17.

Least common multiple of 13 and 17 is 221.

Find the least number which is exactly divisible by 13 and 17.

Least number which is exactly divisible by 13 and 17 is 221.