What is the LCM of 225 and 30 - Find out answer step by step

Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 225 and 30, is defined as the smallest positive integer that is divisible by both. It is written as LCM(225, 30).

Properties of LCM

The LCM of two or more prime numbers is exactly equal to their product.
LCM is associative which means LCM(225, 30) = LCM(30, 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 30 is 450, where 450 is greater than 225 and 30.

Steps to find lcm of 225 and 30 by Listing Method

Find some first multiples of 225 and 30.
Find the least common multiple, and read off the answer!

Example: Find lcm of 225 and 30 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
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 480, 510, 540, 570, 600, 630, 660, 690, 720, 750, 780, 810, 840, 870, 900, 930, 960, 990, 1020, 1050, 1080, 1110, 1140, 1170, 1200, 1230, 1260, 1290, 1320, 1350, 1380, 1410, 1440, 1470, 1500, 1530, 1560, 1590, 1620, 1650, 1680, 1710, 1740, 1770, 1800, 1830, 1860, 1890, 1920, 1950, 1980, 2010, 2040, 2070, 2100, 2130, 2160, 2190, 2220, 2250, 2280, 2310, 2340, 2370, 2400, 2430, 2460, 2490, 2520, 2550, 2580, 2610, 2640, 2670, 2700, 2730, 2760, 2790, 2820, 2850, 2880, 2910, 2940, 2970, 3000, 3030, 3060, 3090, 3120, 3150, 3180, 3210, 3240, 3270, 3300, 3330, 3360, 3390, 3420, 3450, 3480, 3510, 3540, 3570, 3600, 3630, 3660, 3690, 3720, 3750, 3780, 3810, 3840, 3870, 3900, 3930, 3960, 3990, 4020, 4050, 4080, 4110, 4140, 4170, 4200, 4230, 4260, 4290, 4320, 4350, 4380, 4410, 4440, 4470, 4500, 4530, 4560, 4590, 4620, 4650, 4680, 4710, 4740, 4770, 4800, 4830, 4860, 4890, 4920, 4950, 4980, 5010, 5040, 5070, 5100, 5130, 5160, 5190, 5220, 5250, 5280, 5310, 5340, 5370, 5400, 5430, 5460, 5490, 5520, 5550, 5580, 5610, 5640, 5670, 5700, 5730, 5760, 5790, 5820, 5850, 5880, 5910, 5940, 5970, 6000, 6030, 6060, 6090, 6120, 6150, 6180, 6210, 6240, 6270, 6300, 6330, 6360, 6390, 6420, 6450, 6480, 6510, 6540, 6570, 6600, 6630, 6660, 6690, 6720, 6750

Hence, LCM of 225 and 30 is 450.

Steps to find LCM of 225 and 30 by Common Division Method

Find all the prime numbers that would divide 225 and 30 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 225 and 30 by Common Division Method

2	225 30
3	225 15
3	75 5
5	25 5
5	5 1
	1 1

Hence, LCM of 225 and 30 is 2 x 3 x 3 x 5 x 5 = 450.

Steps to find lcm of 225 and 30 by Formula

The formula for LCM is LCM (225, 30) = (225 x 30) / GCF (225, 30)
Apply the formula, and read off the answer!

Example: Find lcm of 225 and 30 by Formula

GCF of 225 and 30 = 15
LCM of 225 and 30 = (225 x 30) / 15
=> 6750 / 15

Hence, LCM of 225 and 30 is 450.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 225 and 30 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 30 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 30.
So, LCM of 225 and 30 is 450.

A shopkeeper sells candies in packet of 225 and chocolates in packet of 30. 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 30.
So, LCM of 225 and 30 is 450.

Boxes that are 225 inches tall are being pilled next to boxes that are 30 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 30.
So, LCM of 225 and 30 is 450.

Sammy's company prints 225 textbooks at a time. Daniel's company prints textbooks in sets of 30 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 30.
So, LCM of 225 and 30 is 450.

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

Greatest common factors or gcf of 225 and 30 is GCF(225, 30) * LCM(225, 30) = (225 x 30) / GCF(225, 30) = 450.

Find the least number which is exactly divisible by 225 and 30.

Least number which is exactly divisible by 225 and 30 is 450.

Find the LCM of 225 and 30 using GCF method.

Greatest common factor or gcf of 225 and 30 is GCF(225, 30) x LCM(225, 30) = (225 x 30) / GCF(225, 30) = 450.

What is LCM of 225 and 30?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 225 and 30 by Listing Method

Example: Find lcm of 225 and 30 by Listing Method

Steps to find LCM of 225 and 30 by Common Division Method

Example: Find lcm of 225 and 30 by Common Division Method

Steps to find lcm of 225 and 30 by Formula

Example: Find lcm of 225 and 30 by Formula

Examples

What is LCM of 225 and 30?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 225 and 30 by Listing Method

Example: Find lcm of 225 and 30 by Listing Method

Steps to find LCM of 225 and 30 by Common Division Method

Example: Find lcm of 225 and 30 by Common Division Method

Steps to find lcm of 225 and 30 by Formula

Example: Find lcm of 225 and 30 by Formula

Examples

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