What is the LCM of 108 and 81 - Find out answer step by step

What does LCM mean in mathematics?

The least common multiple or LCM of two numbers 108 and 81 is defined as the smallest positive integer which is divisible by both of them. It is represented by LCM(108, 81).

Properties of LCM

The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 108 and 81 is 324, where 108 and 81 are less than 324.
LCM is associative which means LCM(108, 81) = LCM(81, 108).
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 108 and 81 by Listing Method

Find some first multiples of 108 and 81.
Find the least common multiple, and read off the answer!

Example: Find lcm of 108 and 81 by Listing Method

Multiples of 108: 108, 216, 324, 432, 540, 648, 756, 864, 972, 1080, 1188, 1296, 1404, 1512, 1620, 1728, 1836, 1944, 2052, 2160, 2268, 2376, 2484, 2592, 2700, 2808, 2916, 3024, 3132, 3240, 3348, 3456, 3564, 3672, 3780, 3888, 3996, 4104, 4212, 4320, 4428, 4536, 4644, 4752, 4860, 4968, 5076, 5184, 5292, 5400, 5508, 5616, 5724, 5832, 5940, 6048, 6156, 6264, 6372, 6480, 6588, 6696, 6804, 6912, 7020, 7128, 7236, 7344, 7452, 7560, 7668, 7776, 7884, 7992, 8100, 8208, 8316, 8424, 8532, 8640, 8748
Multiples of 81: 81, 162, 243, 324, 405, 486, 567, 648, 729, 810, 891, 972, 1053, 1134, 1215, 1296, 1377, 1458, 1539, 1620, 1701, 1782, 1863, 1944, 2025, 2106, 2187, 2268, 2349, 2430, 2511, 2592, 2673, 2754, 2835, 2916, 2997, 3078, 3159, 3240, 3321, 3402, 3483, 3564, 3645, 3726, 3807, 3888, 3969, 4050, 4131, 4212, 4293, 4374, 4455, 4536, 4617, 4698, 4779, 4860, 4941, 5022, 5103, 5184, 5265, 5346, 5427, 5508, 5589, 5670, 5751, 5832, 5913, 5994, 6075, 6156, 6237, 6318, 6399, 6480, 6561, 6642, 6723, 6804, 6885, 6966, 7047, 7128, 7209, 7290, 7371, 7452, 7533, 7614, 7695, 7776, 7857, 7938, 8019, 8100, 8181, 8262, 8343, 8424, 8505, 8586, 8667, 8748

Hence, LCM of 108 and 81 is 324.

Steps to find LCM of 108 and 81 by Common Division Method

Find all the prime numbers that would divide 108 and 81 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 108 and 81 by Common Division Method

2	108 81
2	54 81
3	27 81
3	9 27
3	3 9
3	1 3
	1 1

Hence, LCM of 108 and 81 is 2 x 2 x 3 x 3 x 3 x 3 = 324.

Steps to find lcm of 108 and 81 by Formula

The formula for LCM is LCM (108, 81) = (108 x 81) / GCF (108, 81)
Apply the formula, and read off the answer!

Example: Find lcm of 108 and 81 by Formula

GCF of 108 and 81 = 27
LCM of 108 and 81 = (108 x 81) / 27
=> 8748 / 27

Hence, LCM of 108 and 81 is 324.

Examples

Ram and Deepika are running on a circular track. They start at the same time. They take 108 and 81 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 108 and 81 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 108 and 81.
So, LCM of 108 and 81 is 324.

A shopkeeper sells candies in packet of 108 and chocolates in packet of 81. 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 108 and 81.
So, LCM of 108 and 81 is 324.

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

Greatest common factors or gcf of 108 and 81 is GCF(108, 81) * LCM(108, 81) = (108 x 81) / GCF(108, 81) = 324.

Sammy's company prints 108 textbooks at a time. Daniel's company prints textbooks in sets of 81 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 108 and 81.
So, LCM of 108 and 81 is 324.

Mary exercises every 108 days and Nikki every 81 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 108 and 81 is 324.

Find the least common multiple of 108 and 81.

Least common multiple of 108 and 81 is 324.

Find the least number which is exactly divisible by 108 and 81.

Least number which is exactly divisible by 108 and 81 is 324.

What is LCM of 108 and 81?

How to find lcm of two numbers

What does LCM mean in mathematics?

Properties of LCM

Steps to find lcm of 108 and 81 by Listing Method

Example: Find lcm of 108 and 81 by Listing Method

Steps to find LCM of 108 and 81 by Common Division Method

Example: Find lcm of 108 and 81 by Common Division Method

Steps to find lcm of 108 and 81 by Formula

Example: Find lcm of 108 and 81 by Formula

Examples

What is LCM of 108 and 81?

How to find lcm of two numbers

What does LCM mean in mathematics?

Properties of LCM

Steps to find lcm of 108 and 81 by Listing Method

Example: Find lcm of 108 and 81 by Listing Method

Steps to find LCM of 108 and 81 by Common Division Method

Example: Find lcm of 108 and 81 by Common Division Method

Steps to find lcm of 108 and 81 by Formula

Example: Find lcm of 108 and 81 by Formula

Examples

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