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 96 and 84.

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 96 and 84 is 672, where 96 and 84 are less than 672.
  • LCM is associative which means LCM(96, 84) = LCM(84, 96).
  • 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 or more prime numbers is their product.

Steps to find lcm of 96 and 84 by Listing Method

Example: Find lcm of 96 and 84 by Listing Method

  • Multiples of 96: 96, 192, 288, 384, 480, 576, 672, 768, 864, 960, 1056, 1152, 1248, 1344, 1440, 1536, 1632, 1728, 1824, 1920, 2016, 2112, 2208, 2304, 2400, 2496, 2592, 2688, 2784, 2880, 2976, 3072, 3168, 3264, 3360, 3456, 3552, 3648, 3744, 3840, 3936, 4032, 4128, 4224, 4320, 4416, 4512, 4608, 4704, 4800, 4896, 4992, 5088, 5184, 5280, 5376, 5472, 5568, 5664, 5760, 5856, 5952, 6048, 6144, 6240, 6336, 6432, 6528, 6624, 6720, 6816, 6912, 7008, 7104, 7200, 7296, 7392, 7488, 7584, 7680, 7776, 7872, 7968, 8064
  • Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840, 924, 1008, 1092, 1176, 1260, 1344, 1428, 1512, 1596, 1680, 1764, 1848, 1932, 2016, 2100, 2184, 2268, 2352, 2436, 2520, 2604, 2688, 2772, 2856, 2940, 3024, 3108, 3192, 3276, 3360, 3444, 3528, 3612, 3696, 3780, 3864, 3948, 4032, 4116, 4200, 4284, 4368, 4452, 4536, 4620, 4704, 4788, 4872, 4956, 5040, 5124, 5208, 5292, 5376, 5460, 5544, 5628, 5712, 5796, 5880, 5964, 6048, 6132, 6216, 6300, 6384, 6468, 6552, 6636, 6720, 6804, 6888, 6972, 7056, 7140, 7224, 7308, 7392, 7476, 7560, 7644, 7728, 7812, 7896, 7980, 8064

Hence, LCM of 96 and 84 is 672.

Steps to find LCM of 96 and 84 by Common Division Method

Example: Find lcm of 96 and 84 by Common Division Method

2 96 84
2 48 42
2 24 21
2 12 21
2 6 21
3 3 21
7 1 7
1 1

Hence, LCM of 96 and 84 is 2 x 2 x 2 x 2 x 2 x 3 x 7 = 672.

Steps to find lcm of 96 and 84 by Formula

Example: Find lcm of 96 and 84 by Formula

  • GCF of 96 and 84 = 12
  • LCM of 96 and 84 = (96 x 84) / 12
  • => 8064 / 12

Hence, LCM of 96 and 84 is 672.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 96 and 84 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 96 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 96 and 84.
So, LCM of 96 and 84 is 672.

A shopkeeper sells candies in packet of 96 and chocolates in packet of 84. 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 96 and 84.
So, LCM of 96 and 84 is 672.

Both the cricket team and the rugby team had games, today. The cricket team plays every 96 days and the basketball team plays every 84 days. When will both teams have games on the same day again?

Given that the cricket team plays every 96 days and the basketball team plays every 84 days, so for finding the next time when both teams will play again we need to find the LCM of 96 and 84.
So, LCM of 96 and 84 is 672.

Sammy's company prints 96 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 96 and 84.
So, LCM of 96 and 84 is 672.

Ariel exercises every 96 days and Rubel every 84 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 96 and 84 is 672.

What is the relation between LCM and GCF( Greatest Common Factor)?

Greatest common factors or gcf of 96 and 84 is GCF(96, 84) * LCM(96, 84) = (96 x 84) / GCF(96, 84) = 672.

Find the least number which is exactly divisible by 96 and 84.

Least number which is exactly divisible by 96 and 84 is 672.