What is the LCM of 68 and 102 - Find out answer step by step

What does LCM mean in mathematics?

The least common multiple or LCM of two numbers 68 and 102 is defined as the smallest positive integer which is divisible by both of them. It is represented by LCM(68, 102).

Properties of LCM

The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 68 and 102 is 204, where 68 and 102 are less than 204.
LCM is associative which means LCM(68, 102) = LCM(102, 68).
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 68 and 102 by Listing Method

Find some first multiples of 68 and 102.
Find the least common multiple, and read off the answer!

Example: Find lcm of 68 and 102 by Listing Method

Multiples of 68: 68, 136, 204, 272, 340, 408, 476, 544, 612, 680, 748, 816, 884, 952, 1020, 1088, 1156, 1224, 1292, 1360, 1428, 1496, 1564, 1632, 1700, 1768, 1836, 1904, 1972, 2040, 2108, 2176, 2244, 2312, 2380, 2448, 2516, 2584, 2652, 2720, 2788, 2856, 2924, 2992, 3060, 3128, 3196, 3264, 3332, 3400, 3468, 3536, 3604, 3672, 3740, 3808, 3876, 3944, 4012, 4080, 4148, 4216, 4284, 4352, 4420, 4488, 4556, 4624, 4692, 4760, 4828, 4896, 4964, 5032, 5100, 5168, 5236, 5304, 5372, 5440, 5508, 5576, 5644, 5712, 5780, 5848, 5916, 5984, 6052, 6120, 6188, 6256, 6324, 6392, 6460, 6528, 6596, 6664, 6732, 6800, 6868, 6936
Multiples of 102: 102, 204, 306, 408, 510, 612, 714, 816, 918, 1020, 1122, 1224, 1326, 1428, 1530, 1632, 1734, 1836, 1938, 2040, 2142, 2244, 2346, 2448, 2550, 2652, 2754, 2856, 2958, 3060, 3162, 3264, 3366, 3468, 3570, 3672, 3774, 3876, 3978, 4080, 4182, 4284, 4386, 4488, 4590, 4692, 4794, 4896, 4998, 5100, 5202, 5304, 5406, 5508, 5610, 5712, 5814, 5916, 6018, 6120, 6222, 6324, 6426, 6528, 6630, 6732, 6834, 6936

Hence, LCM of 68 and 102 is 204.

Steps to find LCM of 68 and 102 by Common Division Method

Find all the prime numbers that would divide 68 and 102 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 68 and 102 by Common Division Method

2	68 102
2	34 51
3	17 51
17	17 17
	1 1

Hence, LCM of 68 and 102 is 2 x 2 x 3 x 17 = 204.

Steps to find lcm of 68 and 102 by Formula

The formula for LCM is LCM (68, 102) = (68 x 102) / GCF (68, 102)
Apply the formula, and read off the answer!

Example: Find lcm of 68 and 102 by Formula

GCF of 68 and 102 = 34
LCM of 68 and 102 = (68 x 102) / 34
=> 6936 / 34

Hence, LCM of 68 and 102 is 204.

Examples

Ram and Deepika are running on a circular track. They start at the same time. They take 68 and 102 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 68 and 102 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 68 and 102.
So, LCM of 68 and 102 is 204.

A shopkeeper sells candies in packet of 68 and chocolates in packet of 102. 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 68 and 102.
So, LCM of 68 and 102 is 204.

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

Greatest common factors or gcf of 68 and 102 is GCF(68, 102) * LCM(68, 102) = (68 x 102) / GCF(68, 102) = 204.

Sammy's company prints 68 textbooks at a time. Daniel's company prints textbooks in sets of 102 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 68 and 102.
So, LCM of 68 and 102 is 204.

Mary exercises every 68 days and Nikki every 102 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 68 and 102 is 204.

Find the least common multiple of 68 and 102.

Least common multiple of 68 and 102 is 204.

Find the least number which is exactly divisible by 68 and 102.

Least number which is exactly divisible by 68 and 102 is 204.

What is LCM of 68 and 102?

How to find lcm of two numbers

What does LCM mean in mathematics?

Properties of LCM

Steps to find lcm of 68 and 102 by Listing Method

Example: Find lcm of 68 and 102 by Listing Method

Steps to find LCM of 68 and 102 by Common Division Method

Example: Find lcm of 68 and 102 by Common Division Method

Steps to find lcm of 68 and 102 by Formula

Example: Find lcm of 68 and 102 by Formula

Examples

What is LCM of 68 and 102?

How to find lcm of two numbers

What does LCM mean in mathematics?

Properties of LCM

Steps to find lcm of 68 and 102 by Listing Method

Example: Find lcm of 68 and 102 by Listing Method

Steps to find LCM of 68 and 102 by Common Division Method

Example: Find lcm of 68 and 102 by Common Division Method

Steps to find lcm of 68 and 102 by Formula

Example: Find lcm of 68 and 102 by Formula

Examples

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