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 31 and 40.

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 31 and 40 is 1240, where 31 and 40 are less than 1240.
  • LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(31, 40) = LCM(40, 31).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 31 and 40 by Listing Method

Example: Find lcm of 31 and 40 by Listing Method

  • Multiples of 31: 31, 62, 93, 124, 155, 186, 217, 248, 279, 310, 341, 372, 403, 434, 465, 496, 527, 558, 589, 620, 651, 682, 713, 744, 775, 806, 837, 868, 899, 930, 961, 992, 1023, 1054, 1085, 1116, 1147, 1178, 1209, 1240
  • 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, 1200, 1240

Hence, LCM of 31 and 40 is 1240.

Steps to find LCM of 31 and 40 by Common Division Method

Example: Find lcm of 31 and 40 by Common Division Method

2 31 40
2 31 20
2 31 10
5 31 5
31 31 1
1 1

Hence, LCM of 31 and 40 is 2 x 2 x 2 x 5 x 31 = 1240.

Steps to find lcm of 31 and 40 by Formula

Example: Find lcm of 31 and 40 by Formula

  • GCF of 31 and 40 = 1
  • LCM of 31 and 40 = (31 x 40) / 1
  • => 1240 / 1

Hence, LCM of 31 and 40 is 1240.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 31 and 40 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 31 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 31 and 40.
So, LCM of 31 and 40 is 1240.

Boxes that are 31 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 31 and 40.
So, LCM of 31 and 40 is 1240.

Sammy's company prints 31 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 31 and 40.
So, LCM of 31 and 40 is 1240.

Ariel exercises every 31 days and Rubel every 40 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 31 and 40 is 1240.

Find the LCM of 31 and 40 using GCF method.

Greatest common factor or gcf of 31 and 40 is GCF(31, 40) x LCM(31, 40) = (31 x 40) / GCF(31, 40) = 1240.

Find the least common multiple of 31 and 40.

Least common multiple of 31 and 40 is 1240.

Find the least number which is exactly divisible by 31 and 40.

Least number which is exactly divisible by 31 and 40 is 1240.