What does LCM mean in mathematics?

The least common multiple or LCM of two numbers 63 and 81 is defined as the smallest positive integer which is divisible by both of them. It is represented by LCM(63, 81).

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 63 and 81 is 567, where 63 and 81 are less than 567.
  • 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(63, 81) = LCM(81, 63).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).

Steps to find lcm of 63 and 81 by Listing Method

Example: Find lcm of 63 and 81 by Listing Method

  • Multiples of 63: 63, 126, 189, 252, 315, 378, 441, 504, 567, 630, 693, 756, 819, 882, 945, 1008, 1071, 1134, 1197, 1260, 1323, 1386, 1449, 1512, 1575, 1638, 1701, 1764, 1827, 1890, 1953, 2016, 2079, 2142, 2205, 2268, 2331, 2394, 2457, 2520, 2583, 2646, 2709, 2772, 2835, 2898, 2961, 3024, 3087, 3150, 3213, 3276, 3339, 3402, 3465, 3528, 3591, 3654, 3717, 3780, 3843, 3906, 3969, 4032, 4095, 4158, 4221, 4284, 4347, 4410, 4473, 4536, 4599, 4662, 4725, 4788, 4851, 4914, 4977, 5040, 5103
  • Multiples of 81: 81, 162, 243, 324, 405, 486, 567, 648, 729, 810, 891, 972, 1053, 1134, 1215, 1296, 1377, 1458, 1539, 1620, 1701, 1782, 1863, 1944, 2025, 2106, 2187, 2268, 2349, 2430, 2511, 2592, 2673, 2754, 2835, 2916, 2997, 3078, 3159, 3240, 3321, 3402, 3483, 3564, 3645, 3726, 3807, 3888, 3969, 4050, 4131, 4212, 4293, 4374, 4455, 4536, 4617, 4698, 4779, 4860, 4941, 5022, 5103

Hence, LCM of 63 and 81 is 567.

Steps to find LCM of 63 and 81 by Common Division Method

Example: Find lcm of 63 and 81 by Common Division Method

3 63 81
3 21 27
3 7 9
3 7 3
7 7 1
1 1

Hence, LCM of 63 and 81 is 3 x 3 x 3 x 3 x 7 = 567.

Steps to find lcm of 63 and 81 by Formula

Example: Find lcm of 63 and 81 by Formula

  • GCF of 63 and 81 = 9
  • LCM of 63 and 81 = (63 x 81) / 9
  • => 5103 / 9

Hence, LCM of 63 and 81 is 567.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 63 and 81 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 63 and 81 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 63 and 81.
So, LCM of 63 and 81 is 567.

Boxes that are 63 inches tall are being pilled next to boxes that are 81 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 63 and 81.
So, LCM of 63 and 81 is 567.

Sammy's company prints 63 textbooks at a time. Daniel's company prints textbooks in sets of 81 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 63 and 81.
So, LCM of 63 and 81 is 567.

Ariel exercises every 63 days and Rubel every 81 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 63 and 81 is 567.

Find the LCM of 63 and 81 using GCF method.

Greatest common factor or gcf of 63 and 81 is GCF(63, 81) x LCM(63, 81) = (63 x 81) / GCF(63, 81) = 567.

Find the least common multiple of 63 and 81.

Least common multiple of 63 and 81 is 567.

Find the least number which is exactly divisible by 63 and 81.

Least number which is exactly divisible by 63 and 81 is 567.