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 44 and 68.

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 44 and 68 is 748, where 44 and 68 are less than 748.
  • LCM is associative which means LCM(44, 68) = LCM(68, 44).
  • 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 or more prime numbers is their product.

Steps to find lcm of 44 and 68 by Listing Method

Example: Find lcm of 44 and 68 by Listing Method

  • Multiples of 44: 44, 88, 132, 176, 220, 264, 308, 352, 396, 440, 484, 528, 572, 616, 660, 704, 748, 792, 836, 880, 924, 968, 1012, 1056, 1100, 1144, 1188, 1232, 1276, 1320, 1364, 1408, 1452, 1496, 1540, 1584, 1628, 1672, 1716, 1760, 1804, 1848, 1892, 1936, 1980, 2024, 2068, 2112, 2156, 2200, 2244, 2288, 2332, 2376, 2420, 2464, 2508, 2552, 2596, 2640, 2684, 2728, 2772, 2816, 2860, 2904, 2948, 2992
  • Multiples of 68: 68, 136, 204, 272, 340, 408, 476, 544, 612, 680, 748, 816, 884, 952, 1020, 1088, 1156, 1224, 1292, 1360, 1428, 1496, 1564, 1632, 1700, 1768, 1836, 1904, 1972, 2040, 2108, 2176, 2244, 2312, 2380, 2448, 2516, 2584, 2652, 2720, 2788, 2856, 2924, 2992

Hence, LCM of 44 and 68 is 748.

Steps to find LCM of 44 and 68 by Common Division Method

Example: Find lcm of 44 and 68 by Common Division Method

2 44 68
2 22 34
11 11 17
17 1 17
1 1

Hence, LCM of 44 and 68 is 2 x 2 x 11 x 17 = 748.

Steps to find lcm of 44 and 68 by Formula

Example: Find lcm of 44 and 68 by Formula

  • GCF of 44 and 68 = 4
  • LCM of 44 and 68 = (44 x 68) / 4
  • => 2992 / 4

Hence, LCM of 44 and 68 is 748.

Examples

Ram and Deepika are running on a circular track. They start at the same time. They take 44 and 68 minutes respectively to go round once. Find at what time they will run together?

Ram and Deepika are running on a circular track. They take 44 and 68 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 44 and 68.
So, LCM of 44 and 68 is 748.

A shopkeeper sells candies in packet of 44 and chocolates in packet of 68. 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 44 and 68.
So, LCM of 44 and 68 is 748.

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

Greatest common factors or gcf of 44 and 68 is GCF(44, 68) * LCM(44, 68) = (44 x 68) / GCF(44, 68) = 748.

Sammy's company prints 44 textbooks at a time. Daniel's company prints textbooks in sets of 68 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 44 and 68.
So, LCM of 44 and 68 is 748.

Mary exercises every 44 days and Nikki every 68 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 44 and 68 is 748.

Find the least common multiple of 44 and 68.

Least common multiple of 44 and 68 is 748.

Find the least number which is exactly divisible by 44 and 68.

Least number which is exactly divisible by 44 and 68 is 748.