What is LCM of two numbers?

In mathematics, least common multiple which is commonly known as LCM is defined as the smallest non-zero number which is divisible by both given numbers 36 and 81.

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 36 and 81 is 324, where 36 and 81 are less than 324.
  • LCM is associative which means LCM(36, 81) = LCM(81, 36).
  • 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 36 and 81 by Listing Method

Example: Find lcm of 36 and 81 by Listing Method

  • Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432, 468, 504, 540, 576, 612, 648, 684, 720, 756, 792, 828, 864, 900, 936, 972, 1008, 1044, 1080, 1116, 1152, 1188, 1224, 1260, 1296, 1332, 1368, 1404, 1440, 1476, 1512, 1548, 1584, 1620, 1656, 1692, 1728, 1764, 1800, 1836, 1872, 1908, 1944, 1980, 2016, 2052, 2088, 2124, 2160, 2196, 2232, 2268, 2304, 2340, 2376, 2412, 2448, 2484, 2520, 2556, 2592, 2628, 2664, 2700, 2736, 2772, 2808, 2844, 2880, 2916
  • 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

Hence, LCM of 36 and 81 is 324.

Steps to find LCM of 36 and 81 by Common Division Method

Example: Find lcm of 36 and 81 by Common Division Method

2 36 81
2 18 81
3 9 81
3 3 27
3 1 9
3 1 3
1 1

Hence, LCM of 36 and 81 is 2 x 2 x 3 x 3 x 3 x 3 = 324.

Steps to find lcm of 36 and 81 by Formula

Example: Find lcm of 36 and 81 by Formula

  • GCF of 36 and 81 = 9
  • LCM of 36 and 81 = (36 x 81) / 9
  • => 2916 / 9

Hence, LCM of 36 and 81 is 324.

Examples

Ram and Deepika are running on a circular track. They start at the same time. They take 36 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 36 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 36 and 81.
So, LCM of 36 and 81 is 324.

A shopkeeper sells candies in packet of 36 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 36 and 81.
So, LCM of 36 and 81 is 324.

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

Greatest common factors or gcf of 36 and 81 is GCF(36, 81) * LCM(36, 81) = (36 x 81) / GCF(36, 81) = 324.

Sammy's company prints 36 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 36 and 81.
So, LCM of 36 and 81 is 324.

Mary exercises every 36 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 36 and 81 is 324.

Find the least common multiple of 36 and 81.

Least common multiple of 36 and 81 is 324.

Find the least number which is exactly divisible by 36 and 81.

Least number which is exactly divisible by 36 and 81 is 324.