Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 115 and 22, is defined as the smallest positive integer that is divisible by both. It is written as LCM(115, 22).

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 115 and 22 is 2530, where 115 and 22 are less than 2530.
  • LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(115, 22) = LCM(22, 115).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 115 and 22 by Listing Method

Example: Find lcm of 115 and 22 by Listing Method

  • Multiples of 115: 115, 230, 345, 460, 575, 690, 805, 920, 1035, 1150, 1265, 1380, 1495, 1610, 1725, 1840, 1955, 2070, 2185, 2300, 2415, 2530
  • Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, 220, 242, 264, 286, 308, 330, 352, 374, 396, 418, 440, 462, 484, 506, 528, 550, 572, 594, 616, 638, 660, 682, 704, 726, 748, 770, 792, 814, 836, 858, 880, 902, 924, 946, 968, 990, 1012, 1034, 1056, 1078, 1100, 1122, 1144, 1166, 1188, 1210, 1232, 1254, 1276, 1298, 1320, 1342, 1364, 1386, 1408, 1430, 1452, 1474, 1496, 1518, 1540, 1562, 1584, 1606, 1628, 1650, 1672, 1694, 1716, 1738, 1760, 1782, 1804, 1826, 1848, 1870, 1892, 1914, 1936, 1958, 1980, 2002, 2024, 2046, 2068, 2090, 2112, 2134, 2156, 2178, 2200, 2222, 2244, 2266, 2288, 2310, 2332, 2354, 2376, 2398, 2420, 2442, 2464, 2486, 2508, 2530

Hence, LCM of 115 and 22 is 2530.

Steps to find LCM of 115 and 22 by Common Division Method

Example: Find lcm of 115 and 22 by Common Division Method

2 115 22
5 115 11
11 23 11
23 23 1
1 1

Hence, LCM of 115 and 22 is 2 x 5 x 11 x 23 = 2530.

Steps to find lcm of 115 and 22 by Formula

Example: Find lcm of 115 and 22 by Formula

  • GCF of 115 and 22 = 1
  • LCM of 115 and 22 = (115 x 22) / 1
  • => 2530 / 1

Hence, LCM of 115 and 22 is 2530.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 115 and 22 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 115 and 22 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 115 and 22.
So, LCM of 115 and 22 is 2530.

Both the cricket team and the rugby team had games, today. The cricket team plays every 115 days and the basketball team plays every 22 days. When will both teams have games on the same day again?

Given that the cricket team plays every 115 days and the basketball team plays every 22 days, so for finding the next time when both teams will play again we need to find the LCM of 115 and 22.
So, LCM of 115 and 22 is 2530.

Steve spends 115 dollars every day while George spends 22 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 115 and 22.
So, LCM of 115 and 22 is 2530.

Boxes that are 115 inches tall are being pilled next to boxes that are 22 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 115 and 22.
So, LCM of 115 and 22 is 2530.

Find the LCM of 115 and 22 using GCF method.

Greatest common factor or gcf of 115 and 22 is GCF(115, 22) x LCM(115, 22) = (115 x 22) / GCF(115, 22) = 2530.

Find the least common multiple of 115 and 22.

Least common multiple of 115 and 22 is 2530.

Find the least number which is exactly divisible by 115 and 22.

Least number which is exactly divisible by 115 and 22 is 2530.