Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 540 and 90, is defined as the smallest positive integer that is divisible by both. It is written as LCM(540, 90).

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 540 and 90 is 540, where 540 and 90 are less than 540.
  • LCM is associative which means LCM(540, 90) = LCM(90, 540).
  • 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 540 and 90 by Listing Method

Example: Find lcm of 540 and 90 by Listing Method

  • Multiples of 540: 540, 1080, 1620, 2160, 2700, 3240, 3780, 4320, 4860, 5400, 5940, 6480, 7020, 7560, 8100, 8640, 9180, 9720, 10260, 10800, 11340, 11880, 12420, 12960, 13500, 14040, 14580, 15120, 15660, 16200, 16740, 17280, 17820, 18360, 18900, 19440, 19980, 20520, 21060, 21600, 22140, 22680, 23220, 23760, 24300, 24840, 25380, 25920, 26460, 27000, 27540, 28080, 28620, 29160, 29700, 30240, 30780, 31320, 31860, 32400, 32940, 33480, 34020, 34560, 35100, 35640, 36180, 36720, 37260, 37800, 38340, 38880, 39420, 39960, 40500, 41040, 41580, 42120, 42660, 43200, 43740, 44280, 44820, 45360, 45900, 46440, 46980, 47520, 48060, 48600
  • Multiples of 90: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900, 990, 1080, 1170, 1260, 1350, 1440, 1530, 1620, 1710, 1800, 1890, 1980, 2070, 2160, 2250, 2340, 2430, 2520, 2610, 2700, 2790, 2880, 2970, 3060, 3150, 3240, 3330, 3420, 3510, 3600, 3690, 3780, 3870, 3960, 4050, 4140, 4230, 4320, 4410, 4500, 4590, 4680, 4770, 4860, 4950, 5040, 5130, 5220, 5310, 5400, 5490, 5580, 5670, 5760, 5850, 5940, 6030, 6120, 6210, 6300, 6390, 6480, 6570, 6660, 6750, 6840, 6930, 7020, 7110, 7200, 7290, 7380, 7470, 7560, 7650, 7740, 7830, 7920, 8010, 8100, 8190, 8280, 8370, 8460, 8550, 8640, 8730, 8820, 8910, 9000, 9090, 9180, 9270, 9360, 9450, 9540, 9630, 9720, 9810, 9900, 9990, 10080, 10170, 10260, 10350, 10440, 10530, 10620, 10710, 10800, 10890, 10980, 11070, 11160, 11250, 11340, 11430, 11520, 11610, 11700, 11790, 11880, 11970, 12060, 12150, 12240, 12330, 12420, 12510, 12600, 12690, 12780, 12870, 12960, 13050, 13140, 13230, 13320, 13410, 13500, 13590, 13680, 13770, 13860, 13950, 14040, 14130, 14220, 14310, 14400, 14490, 14580, 14670, 14760, 14850, 14940, 15030, 15120, 15210, 15300, 15390, 15480, 15570, 15660, 15750, 15840, 15930, 16020, 16110, 16200, 16290, 16380, 16470, 16560, 16650, 16740, 16830, 16920, 17010, 17100, 17190, 17280, 17370, 17460, 17550, 17640, 17730, 17820, 17910, 18000, 18090, 18180, 18270, 18360, 18450, 18540, 18630, 18720, 18810, 18900, 18990, 19080, 19170, 19260, 19350, 19440, 19530, 19620, 19710, 19800, 19890, 19980, 20070, 20160, 20250, 20340, 20430, 20520, 20610, 20700, 20790, 20880, 20970, 21060, 21150, 21240, 21330, 21420, 21510, 21600, 21690, 21780, 21870, 21960, 22050, 22140, 22230, 22320, 22410, 22500, 22590, 22680, 22770, 22860, 22950, 23040, 23130, 23220, 23310, 23400, 23490, 23580, 23670, 23760, 23850, 23940, 24030, 24120, 24210, 24300, 24390, 24480, 24570, 24660, 24750, 24840, 24930, 25020, 25110, 25200, 25290, 25380, 25470, 25560, 25650, 25740, 25830, 25920, 26010, 26100, 26190, 26280, 26370, 26460, 26550, 26640, 26730, 26820, 26910, 27000, 27090, 27180, 27270, 27360, 27450, 27540, 27630, 27720, 27810, 27900, 27990, 28080, 28170, 28260, 28350, 28440, 28530, 28620, 28710, 28800, 28890, 28980, 29070, 29160, 29250, 29340, 29430, 29520, 29610, 29700, 29790, 29880, 29970, 30060, 30150, 30240, 30330, 30420, 30510, 30600, 30690, 30780, 30870, 30960, 31050, 31140, 31230, 31320, 31410, 31500, 31590, 31680, 31770, 31860, 31950, 32040, 32130, 32220, 32310, 32400, 32490, 32580, 32670, 32760, 32850, 32940, 33030, 33120, 33210, 33300, 33390, 33480, 33570, 33660, 33750, 33840, 33930, 34020, 34110, 34200, 34290, 34380, 34470, 34560, 34650, 34740, 34830, 34920, 35010, 35100, 35190, 35280, 35370, 35460, 35550, 35640, 35730, 35820, 35910, 36000, 36090, 36180, 36270, 36360, 36450, 36540, 36630, 36720, 36810, 36900, 36990, 37080, 37170, 37260, 37350, 37440, 37530, 37620, 37710, 37800, 37890, 37980, 38070, 38160, 38250, 38340, 38430, 38520, 38610, 38700, 38790, 38880, 38970, 39060, 39150, 39240, 39330, 39420, 39510, 39600, 39690, 39780, 39870, 39960, 40050, 40140, 40230, 40320, 40410, 40500, 40590, 40680, 40770, 40860, 40950, 41040, 41130, 41220, 41310, 41400, 41490, 41580, 41670, 41760, 41850, 41940, 42030, 42120, 42210, 42300, 42390, 42480, 42570, 42660, 42750, 42840, 42930, 43020, 43110, 43200, 43290, 43380, 43470, 43560, 43650, 43740, 43830, 43920, 44010, 44100, 44190, 44280, 44370, 44460, 44550, 44640, 44730, 44820, 44910, 45000, 45090, 45180, 45270, 45360, 45450, 45540, 45630, 45720, 45810, 45900, 45990, 46080, 46170, 46260, 46350, 46440, 46530, 46620, 46710, 46800, 46890, 46980, 47070, 47160, 47250, 47340, 47430, 47520, 47610, 47700, 47790, 47880, 47970, 48060, 48150, 48240, 48330, 48420, 48510, 48600

Hence, LCM of 540 and 90 is 540.

Steps to find LCM of 540 and 90 by Common Division Method

Example: Find lcm of 540 and 90 by Common Division Method

2 540 90
2 270 45
3 135 45
3 45 15
3 15 5
5 5 5
1 1

Hence, LCM of 540 and 90 is 2 x 2 x 3 x 3 x 3 x 5 = 540.

Steps to find lcm of 540 and 90 by Formula

Example: Find lcm of 540 and 90 by Formula

  • GCF of 540 and 90 = 90
  • LCM of 540 and 90 = (540 x 90) / 90
  • => 48600 / 90

Hence, LCM of 540 and 90 is 540.

Examples

Ram and Deepika are running on a circular track. They start at the same time. They take 540 and 90 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 540 and 90 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 540 and 90.
So, LCM of 540 and 90 is 540.

A shopkeeper sells candies in packet of 540 and chocolates in packet of 90. 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 540 and 90.
So, LCM of 540 and 90 is 540.

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

Greatest common factors or gcf of 540 and 90 is GCF(540, 90) * LCM(540, 90) = (540 x 90) / GCF(540, 90) = 540.

Sammy's company prints 540 textbooks at a time. Daniel's company prints textbooks in sets of 90 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 540 and 90.
So, LCM of 540 and 90 is 540.

Mary exercises every 540 days and Nikki every 90 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 540 and 90 is 540.

Find the least common multiple of 540 and 90.

Least common multiple of 540 and 90 is 540.

Find the least number which is exactly divisible by 540 and 90.

Least number which is exactly divisible by 540 and 90 is 540.