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 17 and 7

Properties of LCM

  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(17, 7) = LCM(7, 17).
  • LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
  • The LCM of two given numbers is always greater than the given numbers numbers. Eg- LCM of 17 and 7 is 119, where 119 is greater than 17 and 7.

Steps to find lcm of 17 and 7 by Listing Method

Example: Find lcm of 17 and 7 by Listing Method

  • Multiples of 17: 17, 34, 51, 68, 85, 102, 119
  • Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119

Hence, LCM of 17 and 7 is 119.

Steps to find LCM of 17 and 7 by Common Division Method

Example: Find lcm of 17 and 7 by Common Division Method

7 17 7
17 17 1
1 1

Hence, LCM of 17 and 7 is 7 x 17 = 119.

Steps to find lcm of 17 and 7 by Formula

Example: Find lcm of 17 and 7 by Formula

  • GCF of 17 and 7 = 1
  • LCM of 17 and 7 = (17 x 7) / 1
  • => 119 / 1

Hence, LCM of 17 and 7 is 119.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 17 and 7 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 17 and 7 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 17 and 7.
So, LCM of 17 and 7 is 119.

A shopkeeper sells candies in packet of 17 and chocolates in packet of 7. What is the least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate?

The least number of candies and chocolates Annie should buy so that there will be one candy for each chocolate we need to find the lcm of 17 and 7.
So, LCM of 17 and 7 is 119.

Boxes that are 17 inches tall are being pilled next to boxes that are 7 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 17 and 7.
So, LCM of 17 and 7 is 119.

Sammy's company prints 17 textbooks at a time. Daniel's company prints textbooks in sets of 7 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 17 and 7.
So, LCM of 17 and 7 is 119.

What is the relation between LCM and GCF( Greatest Common Factor)?

Greatest common factors or gcf of 17 and 7 is GCF(17, 7) * LCM(17, 7) = (17 x 7) / GCF(17, 7) = 119.

Find the least number which is exactly divisible by 17 and 7.

Least number which is exactly divisible by 17 and 7 is 119.

Find the LCM of 17 and 7 using GCF method.

Greatest common factor or gcf of 17 and 7 is GCF(17, 7) x LCM(17, 7) = (17 x 7) / GCF(17, 7) = 119.