What is the LCM of 60 and 90 - Find out answer step by step

Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 60 and 90, is defined as the smallest positive integer that is divisible by both. It is written as LCM(60, 90).

Properties of LCM

The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 60 and 90 is 180, where 60 and 90 are less than 180.
LCM is associative which means LCM(60, 90) = LCM(90, 60).
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 or more prime numbers is their product.

Steps to find lcm of 60 and 90 by Listing Method

Find some first multiples of 60 and 90.
Find the least common multiple, and read off the answer!

Example: Find lcm of 60 and 90 by Listing Method

Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, 660, 720, 780, 840, 900, 960, 1020, 1080, 1140, 1200, 1260, 1320, 1380, 1440, 1500, 1560, 1620, 1680, 1740, 1800, 1860, 1920, 1980, 2040, 2100, 2160, 2220, 2280, 2340, 2400, 2460, 2520, 2580, 2640, 2700, 2760, 2820, 2880, 2940, 3000, 3060, 3120, 3180, 3240, 3300, 3360, 3420, 3480, 3540, 3600, 3660, 3720, 3780, 3840, 3900, 3960, 4020, 4080, 4140, 4200, 4260, 4320, 4380, 4440, 4500, 4560, 4620, 4680, 4740, 4800, 4860, 4920, 4980, 5040, 5100, 5160, 5220, 5280, 5340, 5400
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

Hence, LCM of 60 and 90 is 180.

Steps to find LCM of 60 and 90 by Common Division Method

Find all the prime numbers that would divide 60 and 90 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 60 and 90 by Common Division Method

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

Hence, LCM of 60 and 90 is 2 x 2 x 3 x 3 x 5 = 180.

Steps to find lcm of 60 and 90 by Formula

The formula for LCM is LCM (60, 90) = (60 x 90) / GCF (60, 90)
Apply the formula, and read off the answer!

Example: Find lcm of 60 and 90 by Formula

GCF of 60 and 90 = 30
LCM of 60 and 90 = (60 x 90) / 30
=> 5400 / 30

Hence, LCM of 60 and 90 is 180.

Examples

Ram and Deepika are running on a circular track. They start at the same time. They take 60 and 90 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 60 and 90 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 60 and 90.
So, LCM of 60 and 90 is 180.

A shopkeeper sells candies in packet of 60 and chocolates in packet of 90. 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 60 and 90.
So, LCM of 60 and 90 is 180.

What is the relation between LCM and GCF( Greatest Common Factor)?

Greatest common factors or gcf of 60 and 90 is GCF(60, 90) * LCM(60, 90) = (60 x 90) / GCF(60, 90) = 180.

Sammy's company prints 60 textbooks at a time. Daniel's company prints textbooks in sets of 90 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 60 and 90.
So, LCM of 60 and 90 is 180.

Mary exercises every 60 days and Nikki every 90 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 60 and 90 is 180.

Find the least common multiple of 60 and 90.

Least common multiple of 60 and 90 is 180.

Find the least number which is exactly divisible by 60 and 90.

Least number which is exactly divisible by 60 and 90 is 180.

What is LCM of 60 and 90?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 60 and 90 by Listing Method

Example: Find lcm of 60 and 90 by Listing Method

Steps to find LCM of 60 and 90 by Common Division Method

Example: Find lcm of 60 and 90 by Common Division Method

Steps to find lcm of 60 and 90 by Formula

Example: Find lcm of 60 and 90 by Formula

Examples

What is LCM of 60 and 90?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 60 and 90 by Listing Method

Example: Find lcm of 60 and 90 by Listing Method

Steps to find LCM of 60 and 90 by Common Division Method

Example: Find lcm of 60 and 90 by Common Division Method

Steps to find lcm of 60 and 90 by Formula

Example: Find lcm of 60 and 90 by Formula

Examples

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