What does LCM mean in mathematics?

The least common multiple or LCM of two numbers 43 and 22 is defined as the smallest positive integer which is divisible by both of them. It is represented by LCM(43, 22).

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 43 and 22 is 946, where 43 and 22 are less than 946.
  • 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(43, 22) = LCM(22, 43).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 43 and 22 by Listing Method

Example: Find lcm of 43 and 22 by Listing Method

  • Multiples of 43: 43, 86, 129, 172, 215, 258, 301, 344, 387, 430, 473, 516, 559, 602, 645, 688, 731, 774, 817, 860, 903, 946
  • 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

Hence, LCM of 43 and 22 is 946.

Steps to find LCM of 43 and 22 by Common Division Method

Example: Find lcm of 43 and 22 by Common Division Method

2 43 22
11 43 11
43 43 1
1 1

Hence, LCM of 43 and 22 is 2 x 11 x 43 = 946.

Steps to find lcm of 43 and 22 by Formula

Example: Find lcm of 43 and 22 by Formula

  • GCF of 43 and 22 = 1
  • LCM of 43 and 22 = (43 x 22) / 1
  • => 946 / 1

Hence, LCM of 43 and 22 is 946.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 43 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 43 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 43 and 22.
So, LCM of 43 and 22 is 946.

Both the cricket team and the rugby team had games, today. The cricket team plays every 43 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 43 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 43 and 22.
So, LCM of 43 and 22 is 946.

Steve spends 43 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 43 and 22.
So, LCM of 43 and 22 is 946.

Boxes that are 43 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 43 and 22.
So, LCM of 43 and 22 is 946.

Find the LCM of 43 and 22 using GCF method.

Greatest common factor or gcf of 43 and 22 is GCF(43, 22) x LCM(43, 22) = (43 x 22) / GCF(43, 22) = 946.

Find the least common multiple of 43 and 22.

Least common multiple of 43 and 22 is 946.

Find the least number which is exactly divisible by 43 and 22.

Least number which is exactly divisible by 43 and 22 is 946.