# What is LCM of 27 and 72?

LCM of 27 and 72 is 216

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 27 and 72 By Listing Method 3.   Steps to find LCM of 27 and 72 By Common Division Method 4.   Steps to find LCM of 27 and 72 By Formula 5.   Examples

#### 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 72

#### Properties of LCM

• The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 27 and 72 is 216, where 27 and 72 are less than 216.
• 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, 72) = LCM(72, 27).
• LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

### Example: Find lcm of 27 and 72 by Listing Method

• Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, 540, 567, 594, 621, 648, 675, 702, 729, 756, 783, 810, 837, 864, 891, 918, 945, 972, 999, 1026, 1053, 1080, 1107, 1134, 1161, 1188, 1215, 1242, 1269, 1296, 1323, 1350, 1377, 1404, 1431, 1458, 1485, 1512, 1539, 1566, 1593, 1620, 1647, 1674, 1701, 1728, 1755, 1782, 1809, 1836, 1863, 1890, 1917, 1944
• Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720, 792, 864, 936, 1008, 1080, 1152, 1224, 1296, 1368, 1440, 1512, 1584, 1656, 1728, 1800, 1872, 1944

Hence, LCM of 27 and 72 is 216.

### Example: Find lcm of 27 and 72 by Common Division Method

 2 27 72 2 27 36 2 27 18 3 27 9 3 9 3 3 3 1 1 1

Hence, LCM of 27 and 72 is 2 x 2 x 2 x 3 x 3 x 3 = 216.

### Example: Find lcm of 27 and 72 by Formula

• GCF of 27 and 72 = 9
• LCM of 27 and 72 = (27 x 72) / 9
• => 1944 / 9

Hence, LCM of 27 and 72 is 216.

#### Examples

Franky and Joy are running on a circular track. They start at the same time. They take 27 and 72 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 72 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 72.
So, LCM of 27 and 72 is 216.

Both the cricket team and the rugby team had games, today. The cricket team plays every 27 days and the basketball team plays every 72 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 72 days, so for finding the next time when both teams will play again we need to find the LCM of 27 and 72.
So, LCM of 27 and 72 is 216.

Steve spends 27 dollars every day while George spends 72 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 72.
So, LCM of 27 and 72 is 216.

Boxes that are 27 inches tall are being pilled next to boxes that are 72 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 72.
So, LCM of 27 and 72 is 216.

Find the LCM of 27 and 72 using GCF method.

Greatest common factor or gcf of 27 and 72 is GCF(27, 72) x LCM(27, 72) = (27 x 72) / GCF(27, 72) = 216.

Find the least common multiple of 27 and 72.

Least common multiple of 27 and 72 is 216.

Find the least number which is exactly divisible by 27 and 72.

Least number which is exactly divisible by 27 and 72 is 216.