How do we define LCM?

LCM, abbreviation for least common multiple, is defined as the smallest number that is the product of two or more numbers 22 and 45

Properties of LCM

  • LCM follows associative property, that means LCM(22, 45) = LCM(45, 22).
  • 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 22 and 45 is 990, where 22 and 45 are less than 990.
  • The LCM of two or more prime numbers is their product.

Steps to find lcm of 22 and 45 by Listing Method

Example: Find lcm of 22 and 45 by Listing Method

  • Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, 220, 242, 264, 286, 308, 330, 352, 374, 396, 418, 440, 462, 484, 506, 528, 550, 572, 594, 616, 638, 660, 682, 704, 726, 748, 770, 792, 814, 836, 858, 880, 902, 924, 946, 968, 990
  • Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450, 495, 540, 585, 630, 675, 720, 765, 810, 855, 900, 945, 990

Hence, LCM of 22 and 45 is 990.

Steps to find LCM of 22 and 45 by Common Division Method

Example: Find lcm of 22 and 45 by Common Division Method

2 22 45
3 11 45
3 11 15
5 11 5
11 11 1
1 1

Hence, LCM of 22 and 45 is 2 x 3 x 3 x 5 x 11 = 990.

Steps to find lcm of 22 and 45 by Formula

Example: Find lcm of 22 and 45 by Formula

  • GCF of 22 and 45 = 1
  • LCM of 22 and 45 = (22 x 45) / 1
  • => 990 / 1

Hence, LCM of 22 and 45 is 990.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 22 and 45 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 22 and 45 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 22 and 45.
So, LCM of 22 and 45 is 990.

A shopkeeper sells candies in packet of 22 and chocolates in packet of 45. 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 22 and 45.
So, LCM of 22 and 45 is 990.

Both the cricket team and the rugby team had games, today. The cricket team plays every 22 days and the basketball team plays every 45 days. When will both teams have games on the same day again?

Given that the cricket team plays every 22 days and the basketball team plays every 45 days, so for finding the next time when both teams will play again we need to find the LCM of 22 and 45.
So, LCM of 22 and 45 is 990.

Freddy saves 22 dollars every day while Nikki saves 45 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 22 and 45.
So, LCM of 22 and 45 is 990.

Boxes that are 22 inches tall are being pilled next to boxes that are 45 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 22 and 45.
So, LCM of 22 and 45 is 990.

Sammy's company prints 22 textbooks at a time. Daniel's company prints textbooks in sets of 45 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 22 and 45.
So, LCM of 22 and 45 is 990.

Ariel exercises every 22 days and Rubel every 45 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 22 and 45 is 990.