What is LCM of two numbers?

In mathematics, least common multiple which is commonly known as LCM is defined as the smallest non-zero number which is divisible by both given numbers 21 and 84.

Properties of LCM

  • The LCM of two or more prime numbers is exactly equal to their product.
  • LCM is associative which means LCM(21, 84) = LCM(84, 21).
  • LCM is commutative which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
  • LCM is distributive, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
  • The LCM of two given numbers is always greater than the given numbers numbers. Eg- LCM of 21 and 84 is 84, where 84 is greater than 21 and 84.

Steps to find lcm of 21 and 84 by Listing Method

Example: Find lcm of 21 and 84 by Listing Method

  • Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 462, 483, 504, 525, 546, 567, 588, 609, 630, 651, 672, 693, 714, 735, 756, 777, 798, 819, 840, 861, 882, 903, 924, 945, 966, 987, 1008, 1029, 1050, 1071, 1092, 1113, 1134, 1155, 1176, 1197, 1218, 1239, 1260, 1281, 1302, 1323, 1344, 1365, 1386, 1407, 1428, 1449, 1470, 1491, 1512, 1533, 1554, 1575, 1596, 1617, 1638, 1659, 1680, 1701, 1722, 1743, 1764
  • Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840, 924, 1008, 1092, 1176, 1260, 1344, 1428, 1512, 1596, 1680, 1764

Hence, LCM of 21 and 84 is 84.

Steps to find LCM of 21 and 84 by Common Division Method

Example: Find lcm of 21 and 84 by Common Division Method

2 21 84
2 21 42
3 21 21
7 7 7
1 1

Hence, LCM of 21 and 84 is 2 x 2 x 3 x 7 = 84.

Steps to find lcm of 21 and 84 by Formula

Example: Find lcm of 21 and 84 by Formula

  • GCF of 21 and 84 = 21
  • LCM of 21 and 84 = (21 x 84) / 21
  • => 1764 / 21

Hence, LCM of 21 and 84 is 84.

Examples

Steve spends 21 dollars every day while George spends 84 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 21 and 84.
So, LCM of 21 and 84 is 84.

Boxes that are 21 inches tall are being pilled next to boxes that are 84 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 21 and 84.
So, LCM of 21 and 84 is 84.

Sammy's company prints 21 textbooks at a time. Daniel's company prints textbooks in sets of 84 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 21 and 84.
So, LCM of 21 and 84 is 84.

Ram and Deepika are running on a circular track. They start at the same time. They take 21 and 84 minutes respectively to go round once. Find at what time they will run together?

Ram and Deepika are running on a circular track. They take 21 and 84 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 21 and 84.
So, LCM of 21 and 84 is 84.

Find the LCM of 21 and 84 using GCF method.

Greatest common factor or gcf of 21 and 84 is GCF(21, 84) x LCM(21, 84) = (21 x 84) / GCF(21, 84) = 84.

Find the least common multiple of 21 and 84.

Least common multiple of 21 and 84 is 84.

Find the least number which is exactly divisible by 21 and 84.

Least number which is exactly divisible by 21 and 84 is 84.