What is the LCM of 84 and 120 - Find out answer step by step

What is LCM?

In mathematics, least common multiple, which is ordinarily reffered to as LCM is characterized as the smallest non-zero number which is divisible by both given numbers 84 and 120.

Properties of LCM

The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 84 and 120 is 840, where 84 and 120 are less than 840.
LCM is associative which means LCM(84, 120) = LCM(120, 84).
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 84 and 120 by Listing Method

Find some first multiples of 84 and 120.
Find the least common multiple, and read off the answer!

Example: Find lcm of 84 and 120 by Listing Method

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, 8148, 8232, 8316, 8400, 8484, 8568, 8652, 8736, 8820, 8904, 8988, 9072, 9156, 9240, 9324, 9408, 9492, 9576, 9660, 9744, 9828, 9912, 9996, 10080
Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, 1440, 1560, 1680, 1800, 1920, 2040, 2160, 2280, 2400, 2520, 2640, 2760, 2880, 3000, 3120, 3240, 3360, 3480, 3600, 3720, 3840, 3960, 4080, 4200, 4320, 4440, 4560, 4680, 4800, 4920, 5040, 5160, 5280, 5400, 5520, 5640, 5760, 5880, 6000, 6120, 6240, 6360, 6480, 6600, 6720, 6840, 6960, 7080, 7200, 7320, 7440, 7560, 7680, 7800, 7920, 8040, 8160, 8280, 8400, 8520, 8640, 8760, 8880, 9000, 9120, 9240, 9360, 9480, 9600, 9720, 9840, 9960, 10080

Hence, LCM of 84 and 120 is 840.

Steps to find LCM of 84 and 120 by Common Division Method

Find all the prime numbers that would divide 84 and 120 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 84 and 120 by Common Division Method

2	84 120
2	42 60
2	21 30
3	21 15
5	7 5
7	7 1
	1 1

Hence, LCM of 84 and 120 is 2 x 2 x 2 x 3 x 5 x 7 = 840.

Steps to find lcm of 84 and 120 by Formula

The formula for LCM is LCM (84, 120) = (84 x 120) / GCF (84, 120)
Apply the formula, and read off the answer!

Example: Find lcm of 84 and 120 by Formula

GCF of 84 and 120 = 12
LCM of 84 and 120 = (84 x 120) / 12
=> 10080 / 12

Hence, LCM of 84 and 120 is 840.

Examples

Ram and Deepika are running on a circular track. They start at the same time. They take 84 and 120 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 84 and 120 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 84 and 120.
So, LCM of 84 and 120 is 840.

A shopkeeper sells candies in packet of 84 and chocolates in packet of 120. 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 84 and 120.
So, LCM of 84 and 120 is 840.

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

Greatest common factors or gcf of 84 and 120 is GCF(84, 120) * LCM(84, 120) = (84 x 120) / GCF(84, 120) = 840.

Sammy's company prints 84 textbooks at a time. Daniel's company prints textbooks in sets of 120 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 84 and 120.
So, LCM of 84 and 120 is 840.

Mary exercises every 84 days and Nikki every 120 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 84 and 120 is 840.

Find the least common multiple of 84 and 120.

Least common multiple of 84 and 120 is 840.

Find the least number which is exactly divisible by 84 and 120.

Least number which is exactly divisible by 84 and 120 is 840.

What is LCM of 84 and 120?

How to find lcm of two numbers

What is LCM?

Properties of LCM

Steps to find lcm of 84 and 120 by Listing Method

Example: Find lcm of 84 and 120 by Listing Method

Steps to find LCM of 84 and 120 by Common Division Method

Example: Find lcm of 84 and 120 by Common Division Method

Steps to find lcm of 84 and 120 by Formula

Example: Find lcm of 84 and 120 by Formula

Examples

What is LCM of 84 and 120?

How to find lcm of two numbers

What is LCM?

Properties of LCM

Steps to find lcm of 84 and 120 by Listing Method

Example: Find lcm of 84 and 120 by Listing Method

Steps to find LCM of 84 and 120 by Common Division Method

Example: Find lcm of 84 and 120 by Common Division Method

Steps to find lcm of 84 and 120 by Formula

Example: Find lcm of 84 and 120 by Formula

Examples

Recommended

User Also Visited