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 34 and 68.

Properties of LCM

  • LCM follows associative property, that means LCM(34, 68) = LCM(68, 34).
  • LCM follows commutative property, which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • LCM follows distributive property, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 34 and 68 is 68, where 34 and 68 are less than 68.
  • The LCM of two or more prime numbers is their product.

Steps to find lcm of 34 and 68 by Listing Method

Example: Find lcm of 34 and 68 by Listing Method

  • Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340, 374, 408, 442, 476, 510, 544, 578, 612, 646, 680, 714, 748, 782, 816, 850, 884, 918, 952, 986, 1020, 1054, 1088, 1122, 1156, 1190, 1224, 1258, 1292, 1326, 1360, 1394, 1428, 1462, 1496, 1530, 1564, 1598, 1632, 1666, 1700, 1734, 1768, 1802, 1836, 1870, 1904, 1938, 1972, 2006, 2040, 2074, 2108, 2142, 2176, 2210, 2244, 2278, 2312
  • 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

Hence, LCM of 34 and 68 is 68.

Steps to find LCM of 34 and 68 by Common Division Method

Example: Find lcm of 34 and 68 by Common Division Method

2 34 68
2 17 34
17 17 17
1 1

Hence, LCM of 34 and 68 is 2 x 2 x 17 = 68.

Steps to find lcm of 34 and 68 by Formula

Example: Find lcm of 34 and 68 by Formula

  • GCF of 34 and 68 = 34
  • LCM of 34 and 68 = (34 x 68) / 34
  • => 2312 / 34

Hence, LCM of 34 and 68 is 68.

Examples

A shopkeeper sells candies in packet of 34 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 34 and 68.
So, LCM of 34 and 68 is 68.

Both the cricket team and the rugby team had games, today. The cricket team plays every 34 days and the basketball team plays every 68 days. When will both teams have games on the same day again?

Given that the cricket team plays every 34 days and the basketball team plays every 68 days, so for finding the next time when both teams will play again we need to find the LCM of 34 and 68.
So, LCM of 34 and 68 is 68.

Steve spends 34 dollars every day while George spends 68 dollars every day. What is the least number of days it will take each person to spend the same amount of money?

To find the least number of days that would be taken to be able to spend the same amount of dollars we need to find the LCM of 34 and 68.
So, LCM of 34 and 68 is 68.

Sammy's company prints 34 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 34 and 68.
So, LCM of 34 and 68 is 68.

Ariel exercises every 34 days and Rubel 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 34 and 68 is 68.

Find the least common multiple of 34 and 68.

Least common multiple of 34 and 68 is 68.

Find the least number which is exactly divisible by 34 and 68.

Least number which is exactly divisible by 34 and 68 is 68.