What is the LCM of 90 and 75 - Find out answer step by step

Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 90 and 75, is defined as the smallest positive integer that is divisible by both. It is written as LCM(90, 75).

Properties of LCM

LCM follows associative property, that means LCM(90, 75) = LCM(75, 90).
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 90 and 75 is 450, where 90 and 75 are less than 450.
The LCM of two or more prime numbers is their product.

Steps to find lcm of 90 and 75 by Listing Method

Find some first multiples of 90 and 75.
Find the least common multiple, and read off the answer!

Example: Find lcm of 90 and 75 by Listing Method

Multiples of 90: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900, 990, 1080, 1170, 1260, 1350, 1440, 1530, 1620, 1710, 1800, 1890, 1980, 2070, 2160, 2250, 2340, 2430, 2520, 2610, 2700, 2790, 2880, 2970, 3060, 3150, 3240, 3330, 3420, 3510, 3600, 3690, 3780, 3870, 3960, 4050, 4140, 4230, 4320, 4410, 4500, 4590, 4680, 4770, 4860, 4950, 5040, 5130, 5220, 5310, 5400, 5490, 5580, 5670, 5760, 5850, 5940, 6030, 6120, 6210, 6300, 6390, 6480, 6570, 6660, 6750
Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750, 825, 900, 975, 1050, 1125, 1200, 1275, 1350, 1425, 1500, 1575, 1650, 1725, 1800, 1875, 1950, 2025, 2100, 2175, 2250, 2325, 2400, 2475, 2550, 2625, 2700, 2775, 2850, 2925, 3000, 3075, 3150, 3225, 3300, 3375, 3450, 3525, 3600, 3675, 3750, 3825, 3900, 3975, 4050, 4125, 4200, 4275, 4350, 4425, 4500, 4575, 4650, 4725, 4800, 4875, 4950, 5025, 5100, 5175, 5250, 5325, 5400, 5475, 5550, 5625, 5700, 5775, 5850, 5925, 6000, 6075, 6150, 6225, 6300, 6375, 6450, 6525, 6600, 6675, 6750

Hence, LCM of 90 and 75 is 450.

Steps to find LCM of 90 and 75 by Common Division Method

Find all the prime numbers that would divide 90 and 75 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 90 and 75 by Common Division Method

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

Hence, LCM of 90 and 75 is 2 x 3 x 3 x 5 x 5 = 450.

Steps to find lcm of 90 and 75 by Formula

The formula for LCM is LCM (90, 75) = (90 x 75) / GCF (90, 75)
Apply the formula, and read off the answer!

Example: Find lcm of 90 and 75 by Formula

GCF of 90 and 75 = 15
LCM of 90 and 75 = (90 x 75) / 15
=> 6750 / 15

Hence, LCM of 90 and 75 is 450.

Examples

A shopkeeper sells candies in packet of 90 and chocolates in packet of 75. 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 90 and 75.
So, LCM of 90 and 75 is 450.

Both the cricket team and the rugby team had games, today. The cricket team plays every 90 days and the basketball team plays every 75 days. When will both teams have games on the same day again?

Given that the cricket team plays every 90 days and the basketball team plays every 75 days, so for finding the next time when both teams will play again we need to find the LCM of 90 and 75.
So, LCM of 90 and 75 is 450.

Steve spends 90 dollars every day while George spends 75 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 90 and 75.
So, LCM of 90 and 75 is 450.

Sammy's company prints 90 textbooks at a time. Daniel's company prints textbooks in sets of 75 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 90 and 75.
So, LCM of 90 and 75 is 450.

Ariel exercises every 90 days and Rubel every 75 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 90 and 75 is 450.

Find the least common multiple of 90 and 75.

Least common multiple of 90 and 75 is 450.

Find the least number which is exactly divisible by 90 and 75.

Least number which is exactly divisible by 90 and 75 is 450.

What is LCM of 90 and 75?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 90 and 75 by Listing Method

Example: Find lcm of 90 and 75 by Listing Method

Steps to find LCM of 90 and 75 by Common Division Method

Example: Find lcm of 90 and 75 by Common Division Method

Steps to find lcm of 90 and 75 by Formula

Example: Find lcm of 90 and 75 by Formula

Examples

What is LCM of 90 and 75?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 90 and 75 by Listing Method

Example: Find lcm of 90 and 75 by Listing Method

Steps to find LCM of 90 and 75 by Common Division Method

Example: Find lcm of 90 and 75 by Common Division Method

Steps to find lcm of 90 and 75 by Formula

Example: Find lcm of 90 and 75 by Formula

Examples

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