What is the LCM of 225 and 105 - Find out answer step by step

Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 225 and 105, is defined as the smallest positive integer that is divisible by both. It is written as LCM(225, 105).

Properties of LCM

The LCM of two or more prime numbers is exactly equal to their product.
LCM is associative which means LCM(225, 105) = LCM(105, 225).
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 given numbers is always greater than the given numbers numbers. Eg- LCM of 225 and 105 is 1575, where 1575 is greater than 225 and 105.

Steps to find lcm of 225 and 105 by Listing Method

Find some first multiples of 225 and 105.
Find the least common multiple, and read off the answer!

Example: Find lcm of 225 and 105 by Listing Method

Multiples of 225: 225, 450, 675, 900, 1125, 1350, 1575, 1800, 2025, 2250, 2475, 2700, 2925, 3150, 3375, 3600, 3825, 4050, 4275, 4500, 4725, 4950, 5175, 5400, 5625, 5850, 6075, 6300, 6525, 6750, 6975, 7200, 7425, 7650, 7875, 8100, 8325, 8550, 8775, 9000, 9225, 9450, 9675, 9900, 10125, 10350, 10575, 10800, 11025, 11250, 11475, 11700, 11925, 12150, 12375, 12600, 12825, 13050, 13275, 13500, 13725, 13950, 14175, 14400, 14625, 14850, 15075, 15300, 15525, 15750, 15975, 16200, 16425, 16650, 16875, 17100, 17325, 17550, 17775, 18000, 18225, 18450, 18675, 18900, 19125, 19350, 19575, 19800, 20025, 20250, 20475, 20700, 20925, 21150, 21375, 21600, 21825, 22050, 22275, 22500, 22725, 22950, 23175, 23400, 23625
Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050, 1155, 1260, 1365, 1470, 1575, 1680, 1785, 1890, 1995, 2100, 2205, 2310, 2415, 2520, 2625, 2730, 2835, 2940, 3045, 3150, 3255, 3360, 3465, 3570, 3675, 3780, 3885, 3990, 4095, 4200, 4305, 4410, 4515, 4620, 4725, 4830, 4935, 5040, 5145, 5250, 5355, 5460, 5565, 5670, 5775, 5880, 5985, 6090, 6195, 6300, 6405, 6510, 6615, 6720, 6825, 6930, 7035, 7140, 7245, 7350, 7455, 7560, 7665, 7770, 7875, 7980, 8085, 8190, 8295, 8400, 8505, 8610, 8715, 8820, 8925, 9030, 9135, 9240, 9345, 9450, 9555, 9660, 9765, 9870, 9975, 10080, 10185, 10290, 10395, 10500, 10605, 10710, 10815, 10920, 11025, 11130, 11235, 11340, 11445, 11550, 11655, 11760, 11865, 11970, 12075, 12180, 12285, 12390, 12495, 12600, 12705, 12810, 12915, 13020, 13125, 13230, 13335, 13440, 13545, 13650, 13755, 13860, 13965, 14070, 14175, 14280, 14385, 14490, 14595, 14700, 14805, 14910, 15015, 15120, 15225, 15330, 15435, 15540, 15645, 15750, 15855, 15960, 16065, 16170, 16275, 16380, 16485, 16590, 16695, 16800, 16905, 17010, 17115, 17220, 17325, 17430, 17535, 17640, 17745, 17850, 17955, 18060, 18165, 18270, 18375, 18480, 18585, 18690, 18795, 18900, 19005, 19110, 19215, 19320, 19425, 19530, 19635, 19740, 19845, 19950, 20055, 20160, 20265, 20370, 20475, 20580, 20685, 20790, 20895, 21000, 21105, 21210, 21315, 21420, 21525, 21630, 21735, 21840, 21945, 22050, 22155, 22260, 22365, 22470, 22575, 22680, 22785, 22890, 22995, 23100, 23205, 23310, 23415, 23520, 23625

Hence, LCM of 225 and 105 is 1575.

Steps to find LCM of 225 and 105 by Common Division Method

Find all the prime numbers that would divide 225 and 105 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 225 and 105 by Common Division Method

3	225 105
3	75 35
5	25 35
5	5 7
7	1 7
	1 1

Hence, LCM of 225 and 105 is 3 x 3 x 5 x 5 x 7 = 1575.

Steps to find lcm of 225 and 105 by Formula

The formula for LCM is LCM (225, 105) = (225 x 105) / GCF (225, 105)
Apply the formula, and read off the answer!

Example: Find lcm of 225 and 105 by Formula

GCF of 225 and 105 = 15
LCM of 225 and 105 = (225 x 105) / 15
=> 23625 / 15

Hence, LCM of 225 and 105 is 1575.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 225 and 105 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 225 and 105 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 225 and 105.
So, LCM of 225 and 105 is 1575.

A shopkeeper sells candies in packet of 225 and chocolates in packet of 105. 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 225 and 105.
So, LCM of 225 and 105 is 1575.

Boxes that are 225 inches tall are being pilled next to boxes that are 105 inches tall. What is the least height in feet at which the two piles will be the same height?

To find the least height in feet at which the two piles will be at same height we will find LCM of 225 and 105.
So, LCM of 225 and 105 is 1575.

Sammy's company prints 225 textbooks at a time. Daniel's company prints textbooks in sets of 105 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 225 and 105.
So, LCM of 225 and 105 is 1575.

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

Greatest common factors or gcf of 225 and 105 is GCF(225, 105) * LCM(225, 105) = (225 x 105) / GCF(225, 105) = 1575.

Find the least number which is exactly divisible by 225 and 105.

Least number which is exactly divisible by 225 and 105 is 1575.

Find the LCM of 225 and 105 using GCF method.

Greatest common factor or gcf of 225 and 105 is GCF(225, 105) x LCM(225, 105) = (225 x 105) / GCF(225, 105) = 1575.

What is LCM of 225 and 105?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 225 and 105 by Listing Method

Example: Find lcm of 225 and 105 by Listing Method

Steps to find LCM of 225 and 105 by Common Division Method

Example: Find lcm of 225 and 105 by Common Division Method

Steps to find lcm of 225 and 105 by Formula

Example: Find lcm of 225 and 105 by Formula

Examples

What is LCM of 225 and 105?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 225 and 105 by Listing Method

Example: Find lcm of 225 and 105 by Listing Method

Steps to find LCM of 225 and 105 by Common Division Method

Example: Find lcm of 225 and 105 by Common Division Method

Steps to find lcm of 225 and 105 by Formula

Example: Find lcm of 225 and 105 by Formula

Examples

Recommended

User Also Visited