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 9 and 14.

Properties of LCM

  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(9, 14) = LCM(14, 9).
  • 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 9 and 14 is 126, where 126 is greater than 9 and 14.

Steps to find lcm of 9 and 14 by Listing Method

Example: Find lcm of 9 and 14 by Listing Method

  • Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126
  • Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126

Hence, LCM of 9 and 14 is 126.

Steps to find LCM of 9 and 14 by Common Division Method

Example: Find lcm of 9 and 14 by Common Division Method

2 9 14
3 9 7
3 3 7
7 1 7
1 1

Hence, LCM of 9 and 14 is 2 x 3 x 3 x 7 = 126.

Steps to find lcm of 9 and 14 by Formula

Example: Find lcm of 9 and 14 by Formula

  • GCF of 9 and 14 = 1
  • LCM of 9 and 14 = (9 x 14) / 1
  • => 126 / 1

Hence, LCM of 9 and 14 is 126.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 9 and 14 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 9 and 14 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 9 and 14.
So, LCM of 9 and 14 is 126.

A shopkeeper sells candies in packet of 9 and chocolates in packet of 14. 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 9 and 14.
So, LCM of 9 and 14 is 126.

Boxes that are 9 inches tall are being pilled next to boxes that are 14 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 9 and 14.
So, LCM of 9 and 14 is 126.

Sammy's company prints 9 textbooks at a time. Daniel's company prints textbooks in sets of 14 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 9 and 14.
So, LCM of 9 and 14 is 126.

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

Greatest common factors or gcf of 9 and 14 is GCF(9, 14) * LCM(9, 14) = (9 x 14) / GCF(9, 14) = 126.

Find the least number which is exactly divisible by 9 and 14.

Least number which is exactly divisible by 9 and 14 is 126.

Find the LCM of 9 and 14 using GCF method.

Greatest common factor or gcf of 9 and 14 is GCF(9, 14) x LCM(9, 14) = (9 x 14) / GCF(9, 14) = 126.