What is the LCM of 150 and 180 - Find out answer step by step

Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 150 and 180, is defined as the smallest positive integer that is divisible by both. It is written as LCM(150, 180).

Properties of LCM

LCM follows associative property, that means LCM(150, 180) = LCM(180, 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 180 is 900, where 150 and 180 are less than 900.
The LCM of two or more prime numbers is their product.

Steps to find lcm of 150 and 180 by Listing Method

Find some first multiples of 150 and 180.
Find the least common multiple, and read off the answer!

Example: Find lcm of 150 and 180 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
Multiples of 180: 180, 360, 540, 720, 900, 1080, 1260, 1440, 1620, 1800, 1980, 2160, 2340, 2520, 2700, 2880, 3060, 3240, 3420, 3600, 3780, 3960, 4140, 4320, 4500, 4680, 4860, 5040, 5220, 5400, 5580, 5760, 5940, 6120, 6300, 6480, 6660, 6840, 7020, 7200, 7380, 7560, 7740, 7920, 8100, 8280, 8460, 8640, 8820, 9000, 9180, 9360, 9540, 9720, 9900, 10080, 10260, 10440, 10620, 10800, 10980, 11160, 11340, 11520, 11700, 11880, 12060, 12240, 12420, 12600, 12780, 12960, 13140, 13320, 13500, 13680, 13860, 14040, 14220, 14400, 14580, 14760, 14940, 15120, 15300, 15480, 15660, 15840, 16020, 16200, 16380, 16560, 16740, 16920, 17100, 17280, 17460, 17640, 17820, 18000, 18180, 18360, 18540, 18720, 18900, 19080, 19260, 19440, 19620, 19800, 19980, 20160, 20340, 20520, 20700, 20880, 21060, 21240, 21420, 21600, 21780, 21960, 22140, 22320, 22500, 22680, 22860, 23040, 23220, 23400, 23580, 23760, 23940, 24120, 24300, 24480, 24660, 24840, 25020, 25200, 25380, 25560, 25740, 25920, 26100, 26280, 26460, 26640, 26820, 27000

Hence, LCM of 150 and 180 is 900.

Steps to find LCM of 150 and 180 by Common Division Method

Find all the prime numbers that would divide 150 and 180 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 150 and 180 by Common Division Method

2	150 180
2	75 90
3	75 45
3	25 15
5	25 5
5	5 1
	1 1

Hence, LCM of 150 and 180 is 2 x 2 x 3 x 3 x 5 x 5 = 900.

Steps to find lcm of 150 and 180 by Formula

The formula for LCM is LCM (150, 180) = (150 x 180) / GCF (150, 180)
Apply the formula, and read off the answer!

Example: Find lcm of 150 and 180 by Formula

GCF of 150 and 180 = 30
LCM of 150 and 180 = (150 x 180) / 30
=> 27000 / 30

Hence, LCM of 150 and 180 is 900.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 150 and 180 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 180 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 180.
So, LCM of 150 and 180 is 900.

A shopkeeper sells candies in packet of 150 and chocolates in packet of 180. 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 180.
So, LCM of 150 and 180 is 900.

Both the cricket team and the rugby team had games, today. The cricket team plays every 150 days and the basketball team plays every 180 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 180 days, so for finding the next time when both teams will play again we need to find the LCM of 150 and 180.
So, LCM of 150 and 180 is 900.

Freddy saves 150 dollars every day while Nikki saves 180 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 180.
So, LCM of 150 and 180 is 900.

Boxes that are 150 inches tall are being pilled next to boxes that are 180 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 180.
So, LCM of 150 and 180 is 900.

Sammy's company prints 150 textbooks at a time. Daniel's company prints textbooks in sets of 180 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 180.
So, LCM of 150 and 180 is 900.

Ariel exercises every 150 days and Rubel every 180 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 180 is 900.

What is LCM of 150 and 180?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 150 and 180 by Listing Method

Example: Find lcm of 150 and 180 by Listing Method

Steps to find LCM of 150 and 180 by Common Division Method

Example: Find lcm of 150 and 180 by Common Division Method

Steps to find lcm of 150 and 180 by Formula

Example: Find lcm of 150 and 180 by Formula

Examples

What is LCM of 150 and 180?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 150 and 180 by Listing Method

Example: Find lcm of 150 and 180 by Listing Method

Steps to find LCM of 150 and 180 by Common Division Method

Example: Find lcm of 150 and 180 by Common Division Method

Steps to find lcm of 150 and 180 by Formula

Example: Find lcm of 150 and 180 by Formula

Examples

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