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 7 and 9

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 7 and 9 is 63, where 7 and 9 are less than 63.
  • 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(7, 9) = LCM(9, 7).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 7 and 9 by Listing Method

Example: Find lcm of 7 and 9 by Listing Method

  • Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63
  • Multiples of 9: 9, 18, 27, 36, 45, 54, 63

Hence, LCM of 7 and 9 is 63.

Steps to find LCM of 7 and 9 by Common Division Method

Example: Find lcm of 7 and 9 by Common Division Method

3 7 9
3 7 3
7 7 1
1 1

Hence, LCM of 7 and 9 is 3 x 3 x 7 = 63.

Steps to find lcm of 7 and 9 by Formula

Example: Find lcm of 7 and 9 by Formula

  • GCF of 7 and 9 = 1
  • LCM of 7 and 9 = (7 x 9) / 1
  • => 63 / 1

Hence, LCM of 7 and 9 is 63.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 7 and 9 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 7 and 9 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 7 and 9.
So, LCM of 7 and 9 is 63.

Boxes that are 7 inches tall are being pilled next to boxes that are 9 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 7 and 9.
So, LCM of 7 and 9 is 63.

Sammy's company prints 7 textbooks at a time. Daniel's company prints textbooks in sets of 9 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 7 and 9.
So, LCM of 7 and 9 is 63.

Ariel exercises every 7 days and Rubel every 9 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 7 and 9 is 63.

Find the LCM of 7 and 9 using GCF method.

Greatest common factor or gcf of 7 and 9 is GCF(7, 9) x LCM(7, 9) = (7 x 9) / GCF(7, 9) = 63.

Find the least common multiple of 7 and 9.

Least common multiple of 7 and 9 is 63.

Find the least number which is exactly divisible by 7 and 9.

Least number which is exactly divisible by 7 and 9 is 63.