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 85.

Properties of LCM

  • LCM follows associative property, that means LCM(34, 85) = LCM(85, 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 85 is 170, where 34 and 85 are less than 170.
  • The LCM of two or more prime numbers is their product.

Steps to find lcm of 34 and 85 by Listing Method

Example: Find lcm of 34 and 85 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, 2346, 2380, 2414, 2448, 2482, 2516, 2550, 2584, 2618, 2652, 2686, 2720, 2754, 2788, 2822, 2856, 2890
  • Multiples of 85: 85, 170, 255, 340, 425, 510, 595, 680, 765, 850, 935, 1020, 1105, 1190, 1275, 1360, 1445, 1530, 1615, 1700, 1785, 1870, 1955, 2040, 2125, 2210, 2295, 2380, 2465, 2550, 2635, 2720, 2805, 2890

Hence, LCM of 34 and 85 is 170.

Steps to find LCM of 34 and 85 by Common Division Method

Example: Find lcm of 34 and 85 by Common Division Method

2 34 85
5 17 85
17 17 17
1 1

Hence, LCM of 34 and 85 is 2 x 5 x 17 = 170.

Steps to find lcm of 34 and 85 by Formula

Example: Find lcm of 34 and 85 by Formula

  • GCF of 34 and 85 = 17
  • LCM of 34 and 85 = (34 x 85) / 17
  • => 2890 / 17

Hence, LCM of 34 and 85 is 170.

Examples

A shopkeeper sells candies in packet of 34 and chocolates in packet of 85. 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 85.
So, LCM of 34 and 85 is 170.

Both the cricket team and the rugby team had games, today. The cricket team plays every 34 days and the basketball team plays every 85 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 85 days, so for finding the next time when both teams will play again we need to find the LCM of 34 and 85.
So, LCM of 34 and 85 is 170.

Steve spends 34 dollars every day while George spends 85 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 85.
So, LCM of 34 and 85 is 170.

Sammy's company prints 34 textbooks at a time. Daniel's company prints textbooks in sets of 85 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 85.
So, LCM of 34 and 85 is 170.

Ariel exercises every 34 days and Rubel every 85 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 85 is 170.

Find the least common multiple of 34 and 85.

Least common multiple of 34 and 85 is 170.

Find the least number which is exactly divisible by 34 and 85.

Least number which is exactly divisible by 34 and 85 is 170.