# What is LCM of 112 and 196?

LCM of 112 and 196 is 784

#### How to find lcm of two numbers

 1.   What is LCM? 2.   Steps to find LCM of 112 and 196 By Listing Method 3.   Steps to find LCM of 112 and 196 By Common Division Method 4.   Steps to find LCM of 112 and 196 By Formula 5.   Examples

#### 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 112 and 196

#### Properties of LCM

• The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 112 and 196 is 784, where 112 and 196 are less than 784.
• LCM is associative which means LCM(112, 196) = LCM(196, 112).
• 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.

### Example: Find lcm of 112 and 196 by Listing Method

• Multiples of 112: 112, 224, 336, 448, 560, 672, 784, 896, 1008, 1120, 1232, 1344, 1456, 1568, 1680, 1792, 1904, 2016, 2128, 2240, 2352, 2464, 2576, 2688, 2800, 2912, 3024, 3136, 3248, 3360, 3472, 3584, 3696, 3808, 3920, 4032, 4144, 4256, 4368, 4480, 4592, 4704, 4816, 4928, 5040, 5152, 5264, 5376, 5488, 5600, 5712, 5824, 5936, 6048, 6160, 6272, 6384, 6496, 6608, 6720, 6832, 6944, 7056, 7168, 7280, 7392, 7504, 7616, 7728, 7840, 7952, 8064, 8176, 8288, 8400, 8512, 8624, 8736, 8848, 8960, 9072, 9184, 9296, 9408, 9520, 9632, 9744, 9856, 9968, 10080, 10192, 10304, 10416, 10528, 10640, 10752, 10864, 10976, 11088, 11200, 11312, 11424, 11536, 11648, 11760, 11872, 11984, 12096, 12208, 12320, 12432, 12544, 12656, 12768, 12880, 12992, 13104, 13216, 13328, 13440, 13552, 13664, 13776, 13888, 14000, 14112, 14224, 14336, 14448, 14560, 14672, 14784, 14896, 15008, 15120, 15232, 15344, 15456, 15568, 15680, 15792, 15904, 16016, 16128, 16240, 16352, 16464, 16576, 16688, 16800, 16912, 17024, 17136, 17248, 17360, 17472, 17584, 17696, 17808, 17920, 18032, 18144, 18256, 18368, 18480, 18592, 18704, 18816, 18928, 19040, 19152, 19264, 19376, 19488, 19600, 19712, 19824, 19936, 20048, 20160, 20272, 20384, 20496, 20608, 20720, 20832, 20944, 21056, 21168, 21280, 21392, 21504, 21616, 21728, 21840, 21952
• Multiples of 196: 196, 392, 588, 784, 980, 1176, 1372, 1568, 1764, 1960, 2156, 2352, 2548, 2744, 2940, 3136, 3332, 3528, 3724, 3920, 4116, 4312, 4508, 4704, 4900, 5096, 5292, 5488, 5684, 5880, 6076, 6272, 6468, 6664, 6860, 7056, 7252, 7448, 7644, 7840, 8036, 8232, 8428, 8624, 8820, 9016, 9212, 9408, 9604, 9800, 9996, 10192, 10388, 10584, 10780, 10976, 11172, 11368, 11564, 11760, 11956, 12152, 12348, 12544, 12740, 12936, 13132, 13328, 13524, 13720, 13916, 14112, 14308, 14504, 14700, 14896, 15092, 15288, 15484, 15680, 15876, 16072, 16268, 16464, 16660, 16856, 17052, 17248, 17444, 17640, 17836, 18032, 18228, 18424, 18620, 18816, 19012, 19208, 19404, 19600, 19796, 19992, 20188, 20384, 20580, 20776, 20972, 21168, 21364, 21560, 21756, 21952

Hence, LCM of 112 and 196 is 784.

### Example: Find lcm of 112 and 196 by Common Division Method

 2 112 196 2 56 98 2 28 49 2 14 49 7 7 49 7 1 7 1 1

Hence, LCM of 112 and 196 is 2 x 2 x 2 x 2 x 7 x 7 = 784.

### Example: Find lcm of 112 and 196 by Formula

• GCF of 112 and 196 = 28
• LCM of 112 and 196 = (112 x 196) / 28
• => 21952 / 28

Hence, LCM of 112 and 196 is 784.

#### Examples

Franky and Joy are running on a circular track. They start at the same time. They take 112 and 196 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 112 and 196 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 112 and 196.
So, LCM of 112 and 196 is 784.

A shopkeeper sells candies in packet of 112 and chocolates in packet of 196. 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 112 and 196.
So, LCM of 112 and 196 is 784.

Both the cricket team and the rugby team had games, today. The cricket team plays every 112 days and the basketball team plays every 196 days. When will both teams have games on the same day again?

Given that the cricket team plays every 112 days and the basketball team plays every 196 days, so for finding the next time when both teams will play again we need to find the LCM of 112 and 196.
So, LCM of 112 and 196 is 784.

Sammy's company prints 112 textbooks at a time. Daniel's company prints textbooks in sets of 196 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 112 and 196.
So, LCM of 112 and 196 is 784.

Ariel exercises every 112 days and Rubel every 196 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 112 and 196 is 784.

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

Greatest common factors or gcf of 112 and 196 is GCF(112, 196) * LCM(112, 196) = (112 x 196) / GCF(112, 196) = 784.

Find the least number which is exactly divisible by 112 and 196.

Least number which is exactly divisible by 112 and 196 is 784.