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 81 and 18.

Properties of LCM

  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(81, 18) = LCM(18, 81).
  • 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 given numbers is always greater than the given numbers numbers. Eg- LCM of 81 and 18 is 162, where 162 is greater than 81 and 18.

Steps to find lcm of 81 and 18 by Listing Method

Example: Find lcm of 81 and 18 by Listing Method

  • Multiples of 81: 81, 162, 243, 324, 405, 486, 567, 648, 729, 810, 891, 972, 1053, 1134, 1215, 1296, 1377, 1458
  • Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270, 288, 306, 324, 342, 360, 378, 396, 414, 432, 450, 468, 486, 504, 522, 540, 558, 576, 594, 612, 630, 648, 666, 684, 702, 720, 738, 756, 774, 792, 810, 828, 846, 864, 882, 900, 918, 936, 954, 972, 990, 1008, 1026, 1044, 1062, 1080, 1098, 1116, 1134, 1152, 1170, 1188, 1206, 1224, 1242, 1260, 1278, 1296, 1314, 1332, 1350, 1368, 1386, 1404, 1422, 1440, 1458

Hence, LCM of 81 and 18 is 162.

Steps to find LCM of 81 and 18 by Common Division Method

Example: Find lcm of 81 and 18 by Common Division Method

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

Hence, LCM of 81 and 18 is 2 x 3 x 3 x 3 x 3 = 162.

Steps to find lcm of 81 and 18 by Formula

Example: Find lcm of 81 and 18 by Formula

  • GCF of 81 and 18 = 9
  • LCM of 81 and 18 = (81 x 18) / 9
  • => 1458 / 9

Hence, LCM of 81 and 18 is 162.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 81 and 18 minutes respectively to go round once. Find at what time they will run together?

Franky and Joy are running on a circular track. They take 81 and 18 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 81 and 18.
So, LCM of 81 and 18 is 162.

A shopkeeper sells candies in packet of 81 and chocolates in packet of 18. 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 81 and 18.
So, LCM of 81 and 18 is 162.

Boxes that are 81 inches tall are being pilled next to boxes that are 18 inches tall. What is the least height in feet at which the two piles will be the same height?

To find the least height in feet at which the two piles will be at same height we will find LCM of 81 and 18.
So, LCM of 81 and 18 is 162.

Sammy's company prints 81 textbooks at a time. Daniel's company prints textbooks in sets of 18 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 81 and 18.
So, LCM of 81 and 18 is 162.

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

Greatest common factors or gcf of 81 and 18 is GCF(81, 18) * LCM(81, 18) = (81 x 18) / GCF(81, 18) = 162.

Find the least number which is exactly divisible by 81 and 18.

Least number which is exactly divisible by 81 and 18 is 162.

Find the LCM of 81 and 18 using GCF method.

Greatest common factor or gcf of 81 and 18 is GCF(81, 18) x LCM(81, 18) = (81 x 18) / GCF(81, 18) = 162.