What is the LCM of 40 and 900 - Find out answer step by step

Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 40 and 900, is defined as the smallest positive integer that is divisible by both. It is written as LCM(40, 900).

Properties of LCM

The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 40 and 900 is 1800, where 40 and 900 are less than 1800.
LCM is associative which means LCM(40, 900) = LCM(900, 40).
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 40 and 900 by Listing Method

Find some first multiples of 40 and 900.
Find the least common multiple, and read off the answer!

Example: Find lcm of 40 and 900 by Listing Method

Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160, 1200, 1240, 1280, 1320, 1360, 1400, 1440, 1480, 1520, 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840, 1880, 1920, 1960, 2000, 2040, 2080, 2120, 2160, 2200, 2240, 2280, 2320, 2360, 2400, 2440, 2480, 2520, 2560, 2600, 2640, 2680, 2720, 2760, 2800, 2840, 2880, 2920, 2960, 3000, 3040, 3080, 3120, 3160, 3200, 3240, 3280, 3320, 3360, 3400, 3440, 3480, 3520, 3560, 3600, 3640, 3680, 3720, 3760, 3800, 3840, 3880, 3920, 3960, 4000, 4040, 4080, 4120, 4160, 4200, 4240, 4280, 4320, 4360, 4400, 4440, 4480, 4520, 4560, 4600, 4640, 4680, 4720, 4760, 4800, 4840, 4880, 4920, 4960, 5000, 5040, 5080, 5120, 5160, 5200, 5240, 5280, 5320, 5360, 5400, 5440, 5480, 5520, 5560, 5600, 5640, 5680, 5720, 5760, 5800, 5840, 5880, 5920, 5960, 6000, 6040, 6080, 6120, 6160, 6200, 6240, 6280, 6320, 6360, 6400, 6440, 6480, 6520, 6560, 6600, 6640, 6680, 6720, 6760, 6800, 6840, 6880, 6920, 6960, 7000, 7040, 7080, 7120, 7160, 7200, 7240, 7280, 7320, 7360, 7400, 7440, 7480, 7520, 7560, 7600, 7640, 7680, 7720, 7760, 7800, 7840, 7880, 7920, 7960, 8000, 8040, 8080, 8120, 8160, 8200, 8240, 8280, 8320, 8360, 8400, 8440, 8480, 8520, 8560, 8600, 8640, 8680, 8720, 8760, 8800, 8840, 8880, 8920, 8960, 9000, 9040, 9080, 9120, 9160, 9200, 9240, 9280, 9320, 9360, 9400, 9440, 9480, 9520, 9560, 9600, 9640, 9680, 9720, 9760, 9800, 9840, 9880, 9920, 9960, 10000, 10040, 10080, 10120, 10160, 10200, 10240, 10280, 10320, 10360, 10400, 10440, 10480, 10520, 10560, 10600, 10640, 10680, 10720, 10760, 10800, 10840, 10880, 10920, 10960, 11000, 11040, 11080, 11120, 11160, 11200, 11240, 11280, 11320, 11360, 11400, 11440, 11480, 11520, 11560, 11600, 11640, 11680, 11720, 11760, 11800, 11840, 11880, 11920, 11960, 12000, 12040, 12080, 12120, 12160, 12200, 12240, 12280, 12320, 12360, 12400, 12440, 12480, 12520, 12560, 12600, 12640, 12680, 12720, 12760, 12800, 12840, 12880, 12920, 12960, 13000, 13040, 13080, 13120, 13160, 13200, 13240, 13280, 13320, 13360, 13400, 13440, 13480, 13520, 13560, 13600, 13640, 13680, 13720, 13760, 13800, 13840, 13880, 13920, 13960, 14000, 14040, 14080, 14120, 14160, 14200, 14240, 14280, 14320, 14360, 14400, 14440, 14480, 14520, 14560, 14600, 14640, 14680, 14720, 14760, 14800, 14840, 14880, 14920, 14960, 15000, 15040, 15080, 15120, 15160, 15200, 15240, 15280, 15320, 15360, 15400, 15440, 15480, 15520, 15560, 15600, 15640, 15680, 15720, 15760, 15800, 15840, 15880, 15920, 15960, 16000, 16040, 16080, 16120, 16160, 16200, 16240, 16280, 16320, 16360, 16400, 16440, 16480, 16520, 16560, 16600, 16640, 16680, 16720, 16760, 16800, 16840, 16880, 16920, 16960, 17000, 17040, 17080, 17120, 17160, 17200, 17240, 17280, 17320, 17360, 17400, 17440, 17480, 17520, 17560, 17600, 17640, 17680, 17720, 17760, 17800, 17840, 17880, 17920, 17960, 18000, 18040, 18080, 18120, 18160, 18200, 18240, 18280, 18320, 18360, 18400, 18440, 18480, 18520, 18560, 18600, 18640, 18680, 18720, 18760, 18800, 18840, 18880, 18920, 18960, 19000, 19040, 19080, 19120, 19160, 19200, 19240, 19280, 19320, 19360, 19400, 19440, 19480, 19520, 19560, 19600, 19640, 19680, 19720, 19760, 19800, 19840, 19880, 19920, 19960, 20000, 20040, 20080, 20120, 20160, 20200, 20240, 20280, 20320, 20360, 20400, 20440, 20480, 20520, 20560, 20600, 20640, 20680, 20720, 20760, 20800, 20840, 20880, 20920, 20960, 21000, 21040, 21080, 21120, 21160, 21200, 21240, 21280, 21320, 21360, 21400, 21440, 21480, 21520, 21560, 21600, 21640, 21680, 21720, 21760, 21800, 21840, 21880, 21920, 21960, 22000, 22040, 22080, 22120, 22160, 22200, 22240, 22280, 22320, 22360, 22400, 22440, 22480, 22520, 22560, 22600, 22640, 22680, 22720, 22760, 22800, 22840, 22880, 22920, 22960, 23000, 23040, 23080, 23120, 23160, 23200, 23240, 23280, 23320, 23360, 23400, 23440, 23480, 23520, 23560, 23600, 23640, 23680, 23720, 23760, 23800, 23840, 23880, 23920, 23960, 24000, 24040, 24080, 24120, 24160, 24200, 24240, 24280, 24320, 24360, 24400, 24440, 24480, 24520, 24560, 24600, 24640, 24680, 24720, 24760, 24800, 24840, 24880, 24920, 24960, 25000, 25040, 25080, 25120, 25160, 25200, 25240, 25280, 25320, 25360, 25400, 25440, 25480, 25520, 25560, 25600, 25640, 25680, 25720, 25760, 25800, 25840, 25880, 25920, 25960, 26000, 26040, 26080, 26120, 26160, 26200, 26240, 26280, 26320, 26360, 26400, 26440, 26480, 26520, 26560, 26600, 26640, 26680, 26720, 26760, 26800, 26840, 26880, 26920, 26960, 27000, 27040, 27080, 27120, 27160, 27200, 27240, 27280, 27320, 27360, 27400, 27440, 27480, 27520, 27560, 27600, 27640, 27680, 27720, 27760, 27800, 27840, 27880, 27920, 27960, 28000, 28040, 28080, 28120, 28160, 28200, 28240, 28280, 28320, 28360, 28400, 28440, 28480, 28520, 28560, 28600, 28640, 28680, 28720, 28760, 28800, 28840, 28880, 28920, 28960, 29000, 29040, 29080, 29120, 29160, 29200, 29240, 29280, 29320, 29360, 29400, 29440, 29480, 29520, 29560, 29600, 29640, 29680, 29720, 29760, 29800, 29840, 29880, 29920, 29960, 30000, 30040, 30080, 30120, 30160, 30200, 30240, 30280, 30320, 30360, 30400, 30440, 30480, 30520, 30560, 30600, 30640, 30680, 30720, 30760, 30800, 30840, 30880, 30920, 30960, 31000, 31040, 31080, 31120, 31160, 31200, 31240, 31280, 31320, 31360, 31400, 31440, 31480, 31520, 31560, 31600, 31640, 31680, 31720, 31760, 31800, 31840, 31880, 31920, 31960, 32000, 32040, 32080, 32120, 32160, 32200, 32240, 32280, 32320, 32360, 32400, 32440, 32480, 32520, 32560, 32600, 32640, 32680, 32720, 32760, 32800, 32840, 32880, 32920, 32960, 33000, 33040, 33080, 33120, 33160, 33200, 33240, 33280, 33320, 33360, 33400, 33440, 33480, 33520, 33560, 33600, 33640, 33680, 33720, 33760, 33800, 33840, 33880, 33920, 33960, 34000, 34040, 34080, 34120, 34160, 34200, 34240, 34280, 34320, 34360, 34400, 34440, 34480, 34520, 34560, 34600, 34640, 34680, 34720, 34760, 34800, 34840, 34880, 34920, 34960, 35000, 35040, 35080, 35120, 35160, 35200, 35240, 35280, 35320, 35360, 35400, 35440, 35480, 35520, 35560, 35600, 35640, 35680, 35720, 35760, 35800, 35840, 35880, 35920, 35960, 36000
Multiples of 900: 900, 1800, 2700, 3600, 4500, 5400, 6300, 7200, 8100, 9000, 9900, 10800, 11700, 12600, 13500, 14400, 15300, 16200, 17100, 18000, 18900, 19800, 20700, 21600, 22500, 23400, 24300, 25200, 26100, 27000, 27900, 28800, 29700, 30600, 31500, 32400, 33300, 34200, 35100, 36000

Hence, LCM of 40 and 900 is 1800.

Steps to find LCM of 40 and 900 by Common Division Method

Find all the prime numbers that would divide 40 and 900 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 40 and 900 by Common Division Method

2	40 900
2	20 450
2	10 225
3	5 225
3	5 75
5	5 25
5	1 5
	1 1

Hence, LCM of 40 and 900 is 2 x 2 x 2 x 3 x 3 x 5 x 5 = 1800.

Steps to find lcm of 40 and 900 by Formula

The formula for LCM is LCM (40, 900) = (40 x 900) / GCF (40, 900)
Apply the formula, and read off the answer!

Example: Find lcm of 40 and 900 by Formula

GCF of 40 and 900 = 20
LCM of 40 and 900 = (40 x 900) / 20
=> 36000 / 20

Hence, LCM of 40 and 900 is 1800.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 40 and 900 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 40 and 900 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 40 and 900.
So, LCM of 40 and 900 is 1800.

A shopkeeper sells candies in packet of 40 and chocolates in packet of 900. 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 40 and 900.
So, LCM of 40 and 900 is 1800.

Both the cricket team and the rugby team had games, today. The cricket team plays every 40 days and the basketball team plays every 900 days. When will both teams have games on the same day again?

Given that the cricket team plays every 40 days and the basketball team plays every 900 days, so for finding the next time when both teams will play again we need to find the LCM of 40 and 900.
So, LCM of 40 and 900 is 1800.

Sammy's company prints 40 textbooks at a time. Daniel's company prints textbooks in sets of 900 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 40 and 900.
So, LCM of 40 and 900 is 1800.

Ariel exercises every 40 days and Rubel every 900 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 40 and 900 is 1800.

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

Greatest common factors or gcf of 40 and 900 is GCF(40, 900) * LCM(40, 900) = (40 x 900) / GCF(40, 900) = 1800.

Find the least number which is exactly divisible by 40 and 900.

Least number which is exactly divisible by 40 and 900 is 1800.

What is LCM of 40 and 900?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 40 and 900 by Listing Method

Example: Find lcm of 40 and 900 by Listing Method

Steps to find LCM of 40 and 900 by Common Division Method

Example: Find lcm of 40 and 900 by Common Division Method

Steps to find lcm of 40 and 900 by Formula

Example: Find lcm of 40 and 900 by Formula

Examples

What is LCM of 40 and 900?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 40 and 900 by Listing Method

Example: Find lcm of 40 and 900 by Listing Method

Steps to find LCM of 40 and 900 by Common Division Method

Example: Find lcm of 40 and 900 by Common Division Method

Steps to find lcm of 40 and 900 by Formula

Example: Find lcm of 40 and 900 by Formula

Examples

Recommended

User Also Visited