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 29 and 40.

Properties of LCM

  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(29, 40) = LCM(40, 29).
  • 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 29 and 40 is 1160, where 1160 is greater than 29 and 40.

Steps to find lcm of 29 and 40 by Listing Method

Example: Find lcm of 29 and 40 by Listing Method

  • Multiples of 29: 29, 58, 87, 116, 145, 174, 203, 232, 261, 290, 319, 348, 377, 406, 435, 464, 493, 522, 551, 580, 609, 638, 667, 696, 725, 754, 783, 812, 841, 870, 899, 928, 957, 986, 1015, 1044, 1073, 1102, 1131, 1160
  • Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920, 960, 1000, 1040, 1080, 1120, 1160

Hence, LCM of 29 and 40 is 1160.

Steps to find LCM of 29 and 40 by Common Division Method

Example: Find lcm of 29 and 40 by Common Division Method

2 29 40
2 29 20
2 29 10
5 29 5
29 29 1
1 1

Hence, LCM of 29 and 40 is 2 x 2 x 2 x 5 x 29 = 1160.

Steps to find lcm of 29 and 40 by Formula

Example: Find lcm of 29 and 40 by Formula

  • GCF of 29 and 40 = 1
  • LCM of 29 and 40 = (29 x 40) / 1
  • => 1160 / 1

Hence, LCM of 29 and 40 is 1160.

Examples

Steve spends 29 dollars every day while George spends 40 dollars every day. What is the least number of days it will take each person to spend the same amount of money?

To find the least number of days that would be taken to be able to spend the same amount of dollars we need to find the LCM of 29 and 40.
So, LCM of 29 and 40 is 1160.

Boxes that are 29 inches tall are being pilled next to boxes that are 40 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 29 and 40.
So, LCM of 29 and 40 is 1160.

Sammy's company prints 29 textbooks at a time. Daniel's company prints textbooks in sets of 40 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 29 and 40.
So, LCM of 29 and 40 is 1160.

Ram and Deepika are running on a circular track. They start at the same time. They take 29 and 40 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 29 and 40 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 29 and 40.
So, LCM of 29 and 40 is 1160.

Find the LCM of 29 and 40 using GCF method.

Greatest common factor or gcf of 29 and 40 is GCF(29, 40) x LCM(29, 40) = (29 x 40) / GCF(29, 40) = 1160.

Find the least common multiple of 29 and 40.

Least common multiple of 29 and 40 is 1160.

Find the least number which is exactly divisible by 29 and 40.

Least number which is exactly divisible by 29 and 40 is 1160.