# What is LCM of 48 and 72?

LCM of 48 and 72 is 144

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 48 and 72 By Listing Method 3.   Steps to find LCM of 48 and 72 By Common Division Method 4.   Steps to find LCM of 48 and 72 By Formula 5.   Examples

#### What does LCM mean in mathematics?

The least common multiple or LCM of two numbers 48 and 72 is defined as the smallest positive integer which is divisible by both of them. It is represented by LCM(48, 72).

#### Properties of LCM

• The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 48 and 72 is 144, where 48 and 72 are less than 144.
• LCM is associative which means LCM(48, 72) = LCM(72, 48).
• 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 or more prime numbers is their product.

### Example: Find lcm of 48 and 72 by Listing Method

• Multiples of 48: 48, 96, 144, 192, 240, 288, 336, 384, 432, 480, 528, 576, 624, 672, 720, 768, 816, 864, 912, 960, 1008, 1056, 1104, 1152, 1200, 1248, 1296, 1344, 1392, 1440, 1488, 1536, 1584, 1632, 1680, 1728, 1776, 1824, 1872, 1920, 1968, 2016, 2064, 2112, 2160, 2208, 2256, 2304, 2352, 2400, 2448, 2496, 2544, 2592, 2640, 2688, 2736, 2784, 2832, 2880, 2928, 2976, 3024, 3072, 3120, 3168, 3216, 3264, 3312, 3360, 3408, 3456
• 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, 2016, 2088, 2160, 2232, 2304, 2376, 2448, 2520, 2592, 2664, 2736, 2808, 2880, 2952, 3024, 3096, 3168, 3240, 3312, 3384, 3456

Hence, LCM of 48 and 72 is 144.

### Example: Find lcm of 48 and 72 by Common Division Method

 2 48 72 2 24 36 2 12 18 2 6 9 3 3 9 3 1 3 1 1

Hence, LCM of 48 and 72 is 2 x 2 x 2 x 2 x 3 x 3 = 144.

### Example: Find lcm of 48 and 72 by Formula

• GCF of 48 and 72 = 24
• LCM of 48 and 72 = (48 x 72) / 24
• => 3456 / 24

Hence, LCM of 48 and 72 is 144.

#### Examples

Franky and Joy are running on a circular track. They start at the same time. They take 48 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 48 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 48 and 72.
So, LCM of 48 and 72 is 144.

A shopkeeper sells candies in packet of 48 and chocolates in packet of 72. What is the least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate?

The least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate we need to find the lcm of 48 and 72.
So, LCM of 48 and 72 is 144.

Both the cricket team and the rugby team had games, today. The cricket team plays every 48 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 48 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 48 and 72.
So, LCM of 48 and 72 is 144.

Sammy's company prints 48 textbooks at a time. Daniel's company prints textbooks in sets of 72 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 48 and 72.
So, LCM of 48 and 72 is 144.

Ariel exercises every 48 days and Rubel every 72 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 48 and 72 is 144.

What is the relation between LCM and GCF( Greatest Common Factor)?

Greatest common factors or gcf of 48 and 72 is GCF(48, 72) * LCM(48, 72) = (48 x 72) / GCF(48, 72) = 144.

Find the least number which is exactly divisible by 48 and 72.

Least number which is exactly divisible by 48 and 72 is 144.