What is the LCM of 180 and 120 - Find out answer step by step

Definition of LCM

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

Properties of LCM

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

Steps to find lcm of 180 and 120 by Listing Method

Find some first multiples of 180 and 120.
Find the least common multiple, and read off the answer!

Example: Find lcm of 180 and 120 by Listing Method

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
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

Hence, LCM of 180 and 120 is 360.

Steps to find LCM of 180 and 120 by Common Division Method

Find all the prime numbers that would divide 180 and 120 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

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

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

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

Steps to find lcm of 180 and 120 by Formula

The formula for LCM is LCM (180, 120) = (180 x 120) / GCF (180, 120)
Apply the formula, and read off the answer!

Example: Find lcm of 180 and 120 by Formula

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

Hence, LCM of 180 and 120 is 360.

Examples

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

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

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

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

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

Mary exercises every 180 days and Nikki every 120 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 180 and 120 is 360.

Find the least common multiple of 180 and 120.

Least common multiple of 180 and 120 is 360.

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

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

What is LCM of 180 and 120?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 180 and 120 by Listing Method

Example: Find lcm of 180 and 120 by Listing Method

Steps to find LCM of 180 and 120 by Common Division Method

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

Steps to find lcm of 180 and 120 by Formula

Example: Find lcm of 180 and 120 by Formula

Examples

What is LCM of 180 and 120?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 180 and 120 by Listing Method

Example: Find lcm of 180 and 120 by Listing Method

Steps to find LCM of 180 and 120 by Common Division Method

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

Steps to find lcm of 180 and 120 by Formula

Example: Find lcm of 180 and 120 by Formula

Examples

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