# What is LCM of 150 and 225?

LCM of 150 and 225 is 450

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 150 and 225 By Listing Method 3.   Steps to find LCM of 150 and 225 By Common Division Method 4.   Steps to find LCM of 150 and 225 By Formula 5.   Examples

#### Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 150 and 225, is defined as the smallest positive integer that is divisible by both. It is written as LCM(150, 225).

#### Properties of LCM

• LCM follows associative property, that means LCM(150, 225) = LCM(225, 150).
• LCM follows commutative property, which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
• LCM follows distributive property, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
• The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 150 and 225 is 450, where 150 and 225 are less than 450.
• The LCM of two or more prime numbers is their product.

### Example: Find lcm of 150 and 225 by Listing Method

• Multiples of 150: 150, 300, 450, 600, 750, 900, 1050, 1200, 1350, 1500, 1650, 1800, 1950, 2100, 2250, 2400, 2550, 2700, 2850, 3000, 3150, 3300, 3450, 3600, 3750, 3900, 4050, 4200, 4350, 4500, 4650, 4800, 4950, 5100, 5250, 5400, 5550, 5700, 5850, 6000, 6150, 6300, 6450, 6600, 6750, 6900, 7050, 7200, 7350, 7500, 7650, 7800, 7950, 8100, 8250, 8400, 8550, 8700, 8850, 9000, 9150, 9300, 9450, 9600, 9750, 9900, 10050, 10200, 10350, 10500, 10650, 10800, 10950, 11100, 11250, 11400, 11550, 11700, 11850, 12000, 12150, 12300, 12450, 12600, 12750, 12900, 13050, 13200, 13350, 13500, 13650, 13800, 13950, 14100, 14250, 14400, 14550, 14700, 14850, 15000, 15150, 15300, 15450, 15600, 15750, 15900, 16050, 16200, 16350, 16500, 16650, 16800, 16950, 17100, 17250, 17400, 17550, 17700, 17850, 18000, 18150, 18300, 18450, 18600, 18750, 18900, 19050, 19200, 19350, 19500, 19650, 19800, 19950, 20100, 20250, 20400, 20550, 20700, 20850, 21000, 21150, 21300, 21450, 21600, 21750, 21900, 22050, 22200, 22350, 22500, 22650, 22800, 22950, 23100, 23250, 23400, 23550, 23700, 23850, 24000, 24150, 24300, 24450, 24600, 24750, 24900, 25050, 25200, 25350, 25500, 25650, 25800, 25950, 26100, 26250, 26400, 26550, 26700, 26850, 27000, 27150, 27300, 27450, 27600, 27750, 27900, 28050, 28200, 28350, 28500, 28650, 28800, 28950, 29100, 29250, 29400, 29550, 29700, 29850, 30000, 30150, 30300, 30450, 30600, 30750, 30900, 31050, 31200, 31350, 31500, 31650, 31800, 31950, 32100, 32250, 32400, 32550, 32700, 32850, 33000, 33150, 33300, 33450, 33600, 33750
• 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, 23850, 24075, 24300, 24525, 24750, 24975, 25200, 25425, 25650, 25875, 26100, 26325, 26550, 26775, 27000, 27225, 27450, 27675, 27900, 28125, 28350, 28575, 28800, 29025, 29250, 29475, 29700, 29925, 30150, 30375, 30600, 30825, 31050, 31275, 31500, 31725, 31950, 32175, 32400, 32625, 32850, 33075, 33300, 33525, 33750

Hence, LCM of 150 and 225 is 450.

### Example: Find lcm of 150 and 225 by Common Division Method

 2 150 225 3 75 225 3 25 75 5 25 25 5 5 5 1 1

Hence, LCM of 150 and 225 is 2 x 3 x 3 x 5 x 5 = 450.

### Example: Find lcm of 150 and 225 by Formula

• GCF of 150 and 225 = 75
• LCM of 150 and 225 = (150 x 225) / 75
• => 33750 / 75

Hence, LCM of 150 and 225 is 450.

#### Examples

Franky and Joy are running on a circular track. They start at the same time. They take 150 and 225 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 150 and 225 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 150 and 225.
So, LCM of 150 and 225 is 450.

A shopkeeper sells candies in packet of 150 and chocolates in packet of 225. 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 150 and 225.
So, LCM of 150 and 225 is 450.

Both the cricket team and the rugby team had games, today. The cricket team plays every 150 days and the basketball team plays every 225 days. When will both teams have games on the same day again?

Given that the cricket team plays every 150 days and the basketball team plays every 225 days, so for finding the next time when both teams will play again we need to find the LCM of 150 and 225.
So, LCM of 150 and 225 is 450.

Freddy saves 150 dollars every day while Nikki saves 225 dollars every day. What is the least number of days it will take each person to save the same amount of money?

To find the least number of days that would be taken to be able to save the same amount of dollars we need to find the LCM of 150 and 225.
So, LCM of 150 and 225 is 450.

Boxes that are 150 inches tall are being pilled next to boxes that are 225 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 150 and 225.
So, LCM of 150 and 225 is 450.

Sammy's company prints 150 textbooks at a time. Daniel's company prints textbooks in sets of 225 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 150 and 225.
So, LCM of 150 and 225 is 450.

Ariel exercises every 150 days and Rubel every 225 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 150 and 225 is 450.