How do we define LCM?

LCM, abbreviation for least common multiple, is defined as the smallest number that is the product of two or more numbers 12 and 64

Properties of LCM

  • The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 12 and 64 is 192, where 12 and 64 are less than 192.
  • LCM is associative which means LCM(12, 64) = LCM(64, 12).
  • 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 12 and 64 by Listing Method

Example: Find lcm of 12 and 64 by Listing Method

  • Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432, 444, 456, 468, 480, 492, 504, 516, 528, 540, 552, 564, 576, 588, 600, 612, 624, 636, 648, 660, 672, 684, 696, 708, 720, 732, 744, 756, 768
  • Multiples of 64: 64, 128, 192, 256, 320, 384, 448, 512, 576, 640, 704, 768

Hence, LCM of 12 and 64 is 192.

Steps to find LCM of 12 and 64 by Common Division Method

Example: Find lcm of 12 and 64 by Common Division Method

2 12 64
2 6 32
2 3 16
2 3 8
2 3 4
2 3 2
3 3 1
1 1

Hence, LCM of 12 and 64 is 2 x 2 x 2 x 2 x 2 x 2 x 3 = 192.

Steps to find lcm of 12 and 64 by Formula

Example: Find lcm of 12 and 64 by Formula

  • GCF of 12 and 64 = 4
  • LCM of 12 and 64 = (12 x 64) / 4
  • => 768 / 4

Hence, LCM of 12 and 64 is 192.

Examples

Ram and Deepika are running on a circular track. They start at the same time. They take 12 and 64 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 12 and 64 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 12 and 64.
So, LCM of 12 and 64 is 192.

A shopkeeper sells candies in packet of 12 and chocolates in packet of 64. 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 12 and 64.
So, LCM of 12 and 64 is 192.

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

Greatest common factors or gcf of 12 and 64 is GCF(12, 64) * LCM(12, 64) = (12 x 64) / GCF(12, 64) = 192.

Sammy's company prints 12 textbooks at a time. Daniel's company prints textbooks in sets of 64 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 12 and 64.
So, LCM of 12 and 64 is 192.

Mary exercises every 12 days and Nikki every 64 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 12 and 64 is 192.

Find the least common multiple of 12 and 64.

Least common multiple of 12 and 64 is 192.

Find the least number which is exactly divisible by 12 and 64.

Least number which is exactly divisible by 12 and 64 is 192.