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 32.

Properties of LCM

  • LCM follows associative property, that means LCM(14, 32) = LCM(32, 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 32 is 224, where 14 and 32 are less than 224.
  • The LCM of two or more prime numbers is their product.

Steps to find lcm of 14 and 32 by Listing Method

Example: Find lcm of 14 and 32 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
  • Multiples of 32: 32, 64, 96, 128, 160, 192, 224, 256, 288, 320, 352, 384, 416, 448

Hence, LCM of 14 and 32 is 224.

Steps to find LCM of 14 and 32 by Common Division Method

Example: Find lcm of 14 and 32 by Common Division Method

2 14 32
2 7 16
2 7 8
2 7 4
2 7 2
7 7 1
1 1

Hence, LCM of 14 and 32 is 2 x 2 x 2 x 2 x 2 x 7 = 224.

Steps to find lcm of 14 and 32 by Formula

Example: Find lcm of 14 and 32 by Formula

  • GCF of 14 and 32 = 2
  • LCM of 14 and 32 = (14 x 32) / 2
  • => 448 / 2

Hence, LCM of 14 and 32 is 224.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 14 and 32 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 32 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 32.
So, LCM of 14 and 32 is 224.

A shopkeeper sells candies in packet of 14 and chocolates in packet of 32. 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 32.
So, LCM of 14 and 32 is 224.

Both the cricket team and the rugby team had games, today. The cricket team plays every 14 days and the basketball team plays every 32 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 32 days, so for finding the next time when both teams will play again we need to find the LCM of 14 and 32.
So, LCM of 14 and 32 is 224.

Freddy saves 14 dollars every day while Nikki saves 32 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 32.
So, LCM of 14 and 32 is 224.

Boxes that are 14 inches tall are being pilled next to boxes that are 32 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 32.
So, LCM of 14 and 32 is 224.

Sammy's company prints 14 textbooks at a time. Daniel's company prints textbooks in sets of 32 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 32.
So, LCM of 14 and 32 is 224.

Ariel exercises every 14 days and Rubel every 32 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 32 is 224.