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 39 and 13.

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 39 and 13 is 39, where 39 and 13 are less than 39.
  • 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(39, 13) = LCM(13, 39).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 39 and 13 by Listing Method

Example: Find lcm of 39 and 13 by Listing Method

  • Multiples of 39: 39, 78, 117, 156, 195, 234, 273, 312, 351, 390, 429, 468, 507
  • Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 338, 351, 364, 377, 390, 403, 416, 429, 442, 455, 468, 481, 494, 507

Hence, LCM of 39 and 13 is 39.

Steps to find LCM of 39 and 13 by Common Division Method

Example: Find lcm of 39 and 13 by Common Division Method

3 39 13
13 13 13
1 1

Hence, LCM of 39 and 13 is 3 x 13 = 39.

Steps to find lcm of 39 and 13 by Formula

Example: Find lcm of 39 and 13 by Formula

  • GCF of 39 and 13 = 13
  • LCM of 39 and 13 = (39 x 13) / 13
  • => 507 / 13

Hence, LCM of 39 and 13 is 39.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 39 and 13 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 39 and 13 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 39 and 13.
So, LCM of 39 and 13 is 39.

Boxes that are 39 inches tall are being pilled next to boxes that are 13 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 39 and 13.
So, LCM of 39 and 13 is 39.

Sammy's company prints 39 textbooks at a time. Daniel's company prints textbooks in sets of 13 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 39 and 13.
So, LCM of 39 and 13 is 39.

Ariel exercises every 39 days and Rubel every 13 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 39 and 13 is 39.

Find the LCM of 39 and 13 using GCF method.

Greatest common factor or gcf of 39 and 13 is GCF(39, 13) x LCM(39, 13) = (39 x 13) / GCF(39, 13) = 39.

Find the least common multiple of 39 and 13.

Least common multiple of 39 and 13 is 39.

Find the least number which is exactly divisible by 39 and 13.

Least number which is exactly divisible by 39 and 13 is 39.