What is the LCM of 90 and 120 - Find out answer step by step

Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 90 and 120, is defined as the smallest positive integer that is divisible by both. It is written as LCM(90, 120).

Properties of LCM

LCM follows associative property, that means LCM(90, 120) = LCM(120, 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 120 is 360, where 90 and 120 are less than 360.
The LCM of two or more prime numbers is their product.

Steps to find lcm of 90 and 120 by Listing Method

Find some first multiples of 90 and 120.
Find the least common multiple, and read off the answer!

Example: Find lcm of 90 and 120 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, 6840, 6930, 7020, 7110, 7200, 7290, 7380, 7470, 7560, 7650, 7740, 7830, 7920, 8010, 8100, 8190, 8280, 8370, 8460, 8550, 8640, 8730, 8820, 8910, 9000, 9090, 9180, 9270, 9360, 9450, 9540, 9630, 9720, 9810, 9900, 9990, 10080, 10170, 10260, 10350, 10440, 10530, 10620, 10710, 10800
Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, 1440, 1560, 1680, 1800, 1920, 2040, 2160, 2280, 2400, 2520, 2640, 2760, 2880, 3000, 3120, 3240, 3360, 3480, 3600, 3720, 3840, 3960, 4080, 4200, 4320, 4440, 4560, 4680, 4800, 4920, 5040, 5160, 5280, 5400, 5520, 5640, 5760, 5880, 6000, 6120, 6240, 6360, 6480, 6600, 6720, 6840, 6960, 7080, 7200, 7320, 7440, 7560, 7680, 7800, 7920, 8040, 8160, 8280, 8400, 8520, 8640, 8760, 8880, 9000, 9120, 9240, 9360, 9480, 9600, 9720, 9840, 9960, 10080, 10200, 10320, 10440, 10560, 10680, 10800

Hence, LCM of 90 and 120 is 360.

Steps to find LCM of 90 and 120 by Common Division Method

Find all the prime numbers that would divide 90 and 120 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 90 and 120 by Common Division Method

2	90 120
2	45 60
2	45 30
3	45 15
3	15 5
5	5 5
	1 1

Hence, LCM of 90 and 120 is 2 x 2 x 2 x 3 x 3 x 5 = 360.

Steps to find lcm of 90 and 120 by Formula

The formula for LCM is LCM (90, 120) = (90 x 120) / GCF (90, 120)
Apply the formula, and read off the answer!

Example: Find lcm of 90 and 120 by Formula

GCF of 90 and 120 = 30
LCM of 90 and 120 = (90 x 120) / 30
=> 10800 / 30

Hence, LCM of 90 and 120 is 360.

Examples

A shopkeeper sells candies in packet of 90 and chocolates in packet of 120. 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 120.
So, LCM of 90 and 120 is 360.

Both the cricket team and the rugby team had games, today. The cricket team plays every 90 days and the basketball team plays every 120 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 120 days, so for finding the next time when both teams will play again we need to find the LCM of 90 and 120.
So, LCM of 90 and 120 is 360.

Steve spends 90 dollars every day while George spends 120 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 120.
So, LCM of 90 and 120 is 360.

Sammy's company prints 90 textbooks at a time. Daniel's company prints textbooks in sets of 120 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 120.
So, LCM of 90 and 120 is 360.

Ariel exercises every 90 days and Rubel every 120 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 120 is 360.

Find the least common multiple of 90 and 120.

Least common multiple of 90 and 120 is 360.

Find the least number which is exactly divisible by 90 and 120.

Least number which is exactly divisible by 90 and 120 is 360.

What is LCM of 90 and 120?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 90 and 120 by Listing Method

Example: Find lcm of 90 and 120 by Listing Method

Steps to find LCM of 90 and 120 by Common Division Method

Example: Find lcm of 90 and 120 by Common Division Method

Steps to find lcm of 90 and 120 by Formula

Example: Find lcm of 90 and 120 by Formula

Examples

What is LCM of 90 and 120?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 90 and 120 by Listing Method

Example: Find lcm of 90 and 120 by Listing Method

Steps to find LCM of 90 and 120 by Common Division Method

Example: Find lcm of 90 and 120 by Common Division Method

Steps to find lcm of 90 and 120 by Formula

Example: Find lcm of 90 and 120 by Formula

Examples

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