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 21

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 7 and 21 is 21, where 7 and 21 are less than 21.
  • 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, 21) = LCM(21, 7).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 7 and 21 by Listing Method

Example: Find lcm of 7 and 21 by Listing Method

  • Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147
  • Multiples of 21: 21, 42, 63, 84, 105, 126, 147

Hence, LCM of 7 and 21 is 21.

Steps to find LCM of 7 and 21 by Common Division Method

Example: Find lcm of 7 and 21 by Common Division Method

3 7 21
7 7 7
1 1

Hence, LCM of 7 and 21 is 3 x 7 = 21.

Steps to find lcm of 7 and 21 by Formula

Example: Find lcm of 7 and 21 by Formula

  • GCF of 7 and 21 = 7
  • LCM of 7 and 21 = (7 x 21) / 7
  • => 147 / 7

Hence, LCM of 7 and 21 is 21.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 7 and 21 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 21 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 21.
So, LCM of 7 and 21 is 21.

Boxes that are 7 inches tall are being pilled next to boxes that are 21 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 21.
So, LCM of 7 and 21 is 21.

Sammy's company prints 7 textbooks at a time. Daniel's company prints textbooks in sets of 21 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 21.
So, LCM of 7 and 21 is 21.

Ariel exercises every 7 days and Rubel every 21 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 21 is 21.

Find the LCM of 7 and 21 using GCF method.

Greatest common factor or gcf of 7 and 21 is GCF(7, 21) x LCM(7, 21) = (7 x 21) / GCF(7, 21) = 21.

Find the least common multiple of 7 and 21.

Least common multiple of 7 and 21 is 21.

Find the least number which is exactly divisible by 7 and 21.

Least number which is exactly divisible by 7 and 21 is 21.