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 6.

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 39 and 6 is 78, where 39 and 6 are less than 78.
  • 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, 6) = LCM(6, 39).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 39 and 6 by Listing Method

Example: Find lcm of 39 and 6 by Listing Method

  • Multiples of 39: 39, 78, 117, 156, 195, 234
  • Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234

Hence, LCM of 39 and 6 is 78.

Steps to find LCM of 39 and 6 by Common Division Method

Example: Find lcm of 39 and 6 by Common Division Method

2 39 6
3 39 3
13 13 1
1 1

Hence, LCM of 39 and 6 is 2 x 3 x 13 = 78.

Steps to find lcm of 39 and 6 by Formula

Example: Find lcm of 39 and 6 by Formula

  • GCF of 39 and 6 = 3
  • LCM of 39 and 6 = (39 x 6) / 3
  • => 234 / 3

Hence, LCM of 39 and 6 is 78.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 39 and 6 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 6 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 6.
So, LCM of 39 and 6 is 78.

Boxes that are 39 inches tall are being pilled next to boxes that are 6 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 6.
So, LCM of 39 and 6 is 78.

Sammy's company prints 39 textbooks at a time. Daniel's company prints textbooks in sets of 6 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 6.
So, LCM of 39 and 6 is 78.

Ariel exercises every 39 days and Rubel every 6 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 6 is 78.

Find the LCM of 39 and 6 using GCF method.

Greatest common factor or gcf of 39 and 6 is GCF(39, 6) x LCM(39, 6) = (39 x 6) / GCF(39, 6) = 78.

Find the least common multiple of 39 and 6.

Least common multiple of 39 and 6 is 78.

Find the least number which is exactly divisible by 39 and 6.

Least number which is exactly divisible by 39 and 6 is 78.