# What is LCM of 120 and 180?

LCM of 120 and 180 is 360

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 120 and 180 By Listing Method 3.   Steps to find LCM of 120 and 180 By Common Division Method 4.   Steps to find LCM of 120 and 180 By Formula 5.   Examples

#### Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 120 and 180, is defined as the smallest positive integer that is divisible by both. It is written as LCM(120, 180).

#### Properties of LCM

• The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 120 and 180 is 360, where 120 and 180 are less than 360.
• LCM is associative which means LCM(120, 180) = LCM(180, 120).
• 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 120 and 180 by Listing Method

• Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, 1440, 1560, 1680, 1800, 1920, 2040, 2160, 2280, 2400, 2520, 2640, 2760, 2880, 3000, 3120, 3240, 3360, 3480, 3600, 3720, 3840, 3960, 4080, 4200, 4320, 4440, 4560, 4680, 4800, 4920, 5040, 5160, 5280, 5400, 5520, 5640, 5760, 5880, 6000, 6120, 6240, 6360, 6480, 6600, 6720, 6840, 6960, 7080, 7200, 7320, 7440, 7560, 7680, 7800, 7920, 8040, 8160, 8280, 8400, 8520, 8640, 8760, 8880, 9000, 9120, 9240, 9360, 9480, 9600, 9720, 9840, 9960, 10080, 10200, 10320, 10440, 10560, 10680, 10800, 10920, 11040, 11160, 11280, 11400, 11520, 11640, 11760, 11880, 12000, 12120, 12240, 12360, 12480, 12600, 12720, 12840, 12960, 13080, 13200, 13320, 13440, 13560, 13680, 13800, 13920, 14040, 14160, 14280, 14400, 14520, 14640, 14760, 14880, 15000, 15120, 15240, 15360, 15480, 15600, 15720, 15840, 15960, 16080, 16200, 16320, 16440, 16560, 16680, 16800, 16920, 17040, 17160, 17280, 17400, 17520, 17640, 17760, 17880, 18000, 18120, 18240, 18360, 18480, 18600, 18720, 18840, 18960, 19080, 19200, 19320, 19440, 19560, 19680, 19800, 19920, 20040, 20160, 20280, 20400, 20520, 20640, 20760, 20880, 21000, 21120, 21240, 21360, 21480, 21600
• Multiples of 180: 180, 360, 540, 720, 900, 1080, 1260, 1440, 1620, 1800, 1980, 2160, 2340, 2520, 2700, 2880, 3060, 3240, 3420, 3600, 3780, 3960, 4140, 4320, 4500, 4680, 4860, 5040, 5220, 5400, 5580, 5760, 5940, 6120, 6300, 6480, 6660, 6840, 7020, 7200, 7380, 7560, 7740, 7920, 8100, 8280, 8460, 8640, 8820, 9000, 9180, 9360, 9540, 9720, 9900, 10080, 10260, 10440, 10620, 10800, 10980, 11160, 11340, 11520, 11700, 11880, 12060, 12240, 12420, 12600, 12780, 12960, 13140, 13320, 13500, 13680, 13860, 14040, 14220, 14400, 14580, 14760, 14940, 15120, 15300, 15480, 15660, 15840, 16020, 16200, 16380, 16560, 16740, 16920, 17100, 17280, 17460, 17640, 17820, 18000, 18180, 18360, 18540, 18720, 18900, 19080, 19260, 19440, 19620, 19800, 19980, 20160, 20340, 20520, 20700, 20880, 21060, 21240, 21420, 21600

Hence, LCM of 120 and 180 is 360.

### Example: Find lcm of 120 and 180 by Common Division Method

 2 120 180 2 60 90 2 30 45 3 15 45 3 5 15 5 5 5 1 1

Hence, LCM of 120 and 180 is 2 x 2 x 2 x 3 x 3 x 5 = 360.

### Example: Find lcm of 120 and 180 by Formula

• GCF of 120 and 180 = 60
• LCM of 120 and 180 = (120 x 180) / 60
• => 21600 / 60

Hence, LCM of 120 and 180 is 360.

#### Examples

Franky and Joy are running on a circular track. They start at the same time. They take 120 and 180 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 120 and 180 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 120 and 180.
So, LCM of 120 and 180 is 360.

A shopkeeper sells candies in packet of 120 and chocolates in packet of 180. 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 120 and 180.
So, LCM of 120 and 180 is 360.

Both the cricket team and the rugby team had games, today. The cricket team plays every 120 days and the basketball team plays every 180 days. When will both teams have games on the same day again?

Given that the cricket team plays every 120 days and the basketball team plays every 180 days, so for finding the next time when both teams will play again we need to find the LCM of 120 and 180.
So, LCM of 120 and 180 is 360.

Sammy's company prints 120 textbooks at a time. Daniel's company prints textbooks in sets of 180 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 120 and 180.
So, LCM of 120 and 180 is 360.

Ariel exercises every 120 days and Rubel every 180 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 120 and 180 is 360.

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

Greatest common factors or gcf of 120 and 180 is GCF(120, 180) * LCM(120, 180) = (120 x 180) / GCF(120, 180) = 360.

Find the least number which is exactly divisible by 120 and 180.

Least number which is exactly divisible by 120 and 180 is 360.