What is the LCM of 45 and 150 - Find out answer step by step

Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 45 and 150, is defined as the smallest positive integer that is divisible by both. It is written as LCM(45, 150).

Properties of LCM

The LCM of two or more prime numbers is exactly equal to their product.
LCM is associative which means LCM(45, 150) = LCM(150, 45).
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 45 and 150 is 450, where 450 is greater than 45 and 150.

Steps to find lcm of 45 and 150 by Listing Method

Find some first multiples of 45 and 150.
Find the least common multiple, and read off the answer!

Example: Find lcm of 45 and 150 by Listing Method

Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450, 495, 540, 585, 630, 675, 720, 765, 810, 855, 900, 945, 990, 1035, 1080, 1125, 1170, 1215, 1260, 1305, 1350, 1395, 1440, 1485, 1530, 1575, 1620, 1665, 1710, 1755, 1800, 1845, 1890, 1935, 1980, 2025, 2070, 2115, 2160, 2205, 2250, 2295, 2340, 2385, 2430, 2475, 2520, 2565, 2610, 2655, 2700, 2745, 2790, 2835, 2880, 2925, 2970, 3015, 3060, 3105, 3150, 3195, 3240, 3285, 3330, 3375, 3420, 3465, 3510, 3555, 3600, 3645, 3690, 3735, 3780, 3825, 3870, 3915, 3960, 4005, 4050, 4095, 4140, 4185, 4230, 4275, 4320, 4365, 4410, 4455, 4500, 4545, 4590, 4635, 4680, 4725, 4770, 4815, 4860, 4905, 4950, 4995, 5040, 5085, 5130, 5175, 5220, 5265, 5310, 5355, 5400, 5445, 5490, 5535, 5580, 5625, 5670, 5715, 5760, 5805, 5850, 5895, 5940, 5985, 6030, 6075, 6120, 6165, 6210, 6255, 6300, 6345, 6390, 6435, 6480, 6525, 6570, 6615, 6660, 6705, 6750
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

Hence, LCM of 45 and 150 is 450.

Steps to find LCM of 45 and 150 by Common Division Method

Find all the prime numbers that would divide 45 and 150 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 45 and 150 by Common Division Method

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

Hence, LCM of 45 and 150 is 2 x 3 x 3 x 5 x 5 = 450.

Steps to find lcm of 45 and 150 by Formula

The formula for LCM is LCM (45, 150) = (45 x 150) / GCF (45, 150)
Apply the formula, and read off the answer!

Example: Find lcm of 45 and 150 by Formula

GCF of 45 and 150 = 15
LCM of 45 and 150 = (45 x 150) / 15
=> 6750 / 15

Hence, LCM of 45 and 150 is 450.

Examples

Steve spends 45 dollars every day while George spends 150 dollars every day. What is the least number of days it will take each person to spend the same amount of money?

To find the least number of days that would be taken to be able to spend the same amount of dollars we need to find the LCM of 45 and 150.
So, LCM of 45 and 150 is 450.

Boxes that are 45 inches tall are being pilled next to boxes that are 150 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 45 and 150.
So, LCM of 45 and 150 is 450.

Sammy's company prints 45 textbooks at a time. Daniel's company prints textbooks in sets of 150 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 45 and 150.
So, LCM of 45 and 150 is 450.

Ram and Deepika are running on a circular track. They start at the same time. They take 45 and 150 minutes respectively to go round once. Find at what time they will run together?

Ram and Deepika are running on a circular track. They take 45 and 150 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 45 and 150.
So, LCM of 45 and 150 is 450.

Find the LCM of 45 and 150 using GCF method.

Greatest common factor or gcf of 45 and 150 is GCF(45, 150) x LCM(45, 150) = (45 x 150) / GCF(45, 150) = 450.

Find the least common multiple of 45 and 150.

Least common multiple of 45 and 150 is 450.

Find the least number which is exactly divisible by 45 and 150.

Least number which is exactly divisible by 45 and 150 is 450.

What is LCM of 45 and 150?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 45 and 150 by Listing Method

Example: Find lcm of 45 and 150 by Listing Method

Steps to find LCM of 45 and 150 by Common Division Method

Example: Find lcm of 45 and 150 by Common Division Method

Steps to find lcm of 45 and 150 by Formula

Example: Find lcm of 45 and 150 by Formula

Examples

What is LCM of 45 and 150?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 45 and 150 by Listing Method

Example: Find lcm of 45 and 150 by Listing Method

Steps to find LCM of 45 and 150 by Common Division Method

Example: Find lcm of 45 and 150 by Common Division Method

Steps to find lcm of 45 and 150 by Formula

Example: Find lcm of 45 and 150 by Formula

Examples

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