What is LCM?

In mathematics, least common multiple, which is ordinarily reffered to as LCM is characterized as the smallest non-zero number which is divisible by both given numbers 14 and 84.

Properties of LCM

  • LCM follows associative property, that means LCM(14, 84) = LCM(84, 14).
  • 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 14 and 84 is 84, where 14 and 84 are less than 84.
  • The LCM of two or more prime numbers is their product.

Steps to find lcm of 14 and 84 by Listing Method

Example: Find lcm of 14 and 84 by Listing Method

  • Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294, 308, 322, 336, 350, 364, 378, 392, 406, 420, 434, 448, 462, 476, 490, 504, 518, 532, 546, 560, 574, 588, 602, 616, 630, 644, 658, 672, 686, 700, 714, 728, 742, 756, 770, 784, 798, 812, 826, 840, 854, 868, 882, 896, 910, 924, 938, 952, 966, 980, 994, 1008, 1022, 1036, 1050, 1064, 1078, 1092, 1106, 1120, 1134, 1148, 1162, 1176
  • Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840, 924, 1008, 1092, 1176

Hence, LCM of 14 and 84 is 84.

Steps to find LCM of 14 and 84 by Common Division Method

Example: Find lcm of 14 and 84 by Common Division Method

2 14 84
2 7 42
3 7 21
7 7 7
1 1

Hence, LCM of 14 and 84 is 2 x 2 x 3 x 7 = 84.

Steps to find lcm of 14 and 84 by Formula

Example: Find lcm of 14 and 84 by Formula

  • GCF of 14 and 84 = 14
  • LCM of 14 and 84 = (14 x 84) / 14
  • => 1176 / 14

Hence, LCM of 14 and 84 is 84.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 14 and 84 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 14 and 84 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 14 and 84.
So, LCM of 14 and 84 is 84.

A shopkeeper sells candies in packet of 14 and chocolates in packet of 84. 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 14 and 84.
So, LCM of 14 and 84 is 84.

Both the cricket team and the rugby team had games, today. The cricket team plays every 14 days and the basketball team plays every 84 days. When will both teams have games on the same day again?

Given that the cricket team plays every 14 days and the basketball team plays every 84 days, so for finding the next time when both teams will play again we need to find the LCM of 14 and 84.
So, LCM of 14 and 84 is 84.

Freddy saves 14 dollars every day while Nikki saves 84 dollars every day. What is the least number of days it will take each person to save the same amount of money?

To find the least number of days that would be taken to be able to save the same amount of dollars we need to find the LCM of 14 and 84.
So, LCM of 14 and 84 is 84.

Boxes that are 14 inches tall are being pilled next to boxes that are 84 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 14 and 84.
So, LCM of 14 and 84 is 84.

Sammy's company prints 14 textbooks at a time. Daniel's company prints textbooks in sets of 84 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 14 and 84.
So, LCM of 14 and 84 is 84.

Ariel exercises every 14 days and Rubel every 84 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 14 and 84 is 84.