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 49 and 28.

Properties of LCM

  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(49, 28) = LCM(28, 49).
  • 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 49 and 28 is 196, where 196 is greater than 49 and 28.

Steps to find lcm of 49 and 28 by Listing Method

Example: Find lcm of 49 and 28 by Listing Method

  • Multiples of 49: 49, 98, 147, 196, 245, 294, 343, 392, 441, 490, 539, 588, 637, 686, 735, 784, 833, 882, 931, 980, 1029, 1078, 1127, 1176, 1225, 1274, 1323, 1372
  • Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, 336, 364, 392, 420, 448, 476, 504, 532, 560, 588, 616, 644, 672, 700, 728, 756, 784, 812, 840, 868, 896, 924, 952, 980, 1008, 1036, 1064, 1092, 1120, 1148, 1176, 1204, 1232, 1260, 1288, 1316, 1344, 1372

Hence, LCM of 49 and 28 is 196.

Steps to find LCM of 49 and 28 by Common Division Method

Example: Find lcm of 49 and 28 by Common Division Method

2 49 28
2 49 14
7 49 7
7 7 1
1 1

Hence, LCM of 49 and 28 is 2 x 2 x 7 x 7 = 196.

Steps to find lcm of 49 and 28 by Formula

Example: Find lcm of 49 and 28 by Formula

  • GCF of 49 and 28 = 7
  • LCM of 49 and 28 = (49 x 28) / 7
  • => 1372 / 7

Hence, LCM of 49 and 28 is 196.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 49 and 28 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 49 and 28 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 49 and 28.
So, LCM of 49 and 28 is 196.

A shopkeeper sells candies in packet of 49 and chocolates in packet of 28. 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 49 and 28.
So, LCM of 49 and 28 is 196.

Boxes that are 49 inches tall are being pilled next to boxes that are 28 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 49 and 28.
So, LCM of 49 and 28 is 196.

Sammy's company prints 49 textbooks at a time. Daniel's company prints textbooks in sets of 28 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 49 and 28.
So, LCM of 49 and 28 is 196.

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

Greatest common factors or gcf of 49 and 28 is GCF(49, 28) * LCM(49, 28) = (49 x 28) / GCF(49, 28) = 196.

Find the least number which is exactly divisible by 49 and 28.

Least number which is exactly divisible by 49 and 28 is 196.

Find the LCM of 49 and 28 using GCF method.

Greatest common factor or gcf of 49 and 28 is GCF(49, 28) x LCM(49, 28) = (49 x 28) / GCF(49, 28) = 196.