What is the LCM of 105 and 120 - Find out answer step by step

Definition of LCM

LCM stands for least common multiple. In mathematics, LCM of two numbers 105 and 120, is defined as the smallest positive integer that is divisible by both. It is written as LCM(105, 120).

Properties of LCM

The LCM of two or more prime numbers is exactly equal to their product.
LCM is associative which means LCM(105, 120) = LCM(120, 105).
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 given numbers is always greater than the given numbers numbers. Eg- LCM of 105 and 120 is 840, where 840 is greater than 105 and 120.

Steps to find lcm of 105 and 120 by Listing Method

Find some first multiples of 105 and 120.
Find the least common multiple, and read off the answer!

Example: Find lcm of 105 and 120 by Listing Method

Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050, 1155, 1260, 1365, 1470, 1575, 1680, 1785, 1890, 1995, 2100, 2205, 2310, 2415, 2520, 2625, 2730, 2835, 2940, 3045, 3150, 3255, 3360, 3465, 3570, 3675, 3780, 3885, 3990, 4095, 4200, 4305, 4410, 4515, 4620, 4725, 4830, 4935, 5040, 5145, 5250, 5355, 5460, 5565, 5670, 5775, 5880, 5985, 6090, 6195, 6300, 6405, 6510, 6615, 6720, 6825, 6930, 7035, 7140, 7245, 7350, 7455, 7560, 7665, 7770, 7875, 7980, 8085, 8190, 8295, 8400, 8505, 8610, 8715, 8820, 8925, 9030, 9135, 9240, 9345, 9450, 9555, 9660, 9765, 9870, 9975, 10080, 10185, 10290, 10395, 10500, 10605, 10710, 10815, 10920, 11025, 11130, 11235, 11340, 11445, 11550, 11655, 11760, 11865, 11970, 12075, 12180, 12285, 12390, 12495, 12600
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, 10200, 10320, 10440, 10560, 10680, 10800, 10920, 11040, 11160, 11280, 11400, 11520, 11640, 11760, 11880, 12000, 12120, 12240, 12360, 12480, 12600

Hence, LCM of 105 and 120 is 840.

Steps to find LCM of 105 and 120 by Common Division Method

Find all the prime numbers that would divide 105 and 120 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 105 and 120 by Common Division Method

2	105 120
2	105 60
2	105 30
3	105 15
5	35 5
7	7 1
	1 1

Hence, LCM of 105 and 120 is 2 x 2 x 2 x 3 x 5 x 7 = 840.

Steps to find lcm of 105 and 120 by Formula

The formula for LCM is LCM (105, 120) = (105 x 120) / GCF (105, 120)
Apply the formula, and read off the answer!

Example: Find lcm of 105 and 120 by Formula

GCF of 105 and 120 = 15
LCM of 105 and 120 = (105 x 120) / 15
=> 12600 / 15

Hence, LCM of 105 and 120 is 840.

Examples

Franky and Joy are running on a circular track. They start at the same time. They take 105 and 120 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 105 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 105 and 120.
So, LCM of 105 and 120 is 840.

A shopkeeper sells candies in packet of 105 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 105 and 120.
So, LCM of 105 and 120 is 840.

Boxes that are 105 inches tall are being pilled next to boxes that are 120 inches tall. What is the least height in feet at which the two piles will be the same height?

To find the least height in feet at which the two piles will be at same height we will find LCM of 105 and 120.
So, LCM of 105 and 120 is 840.

Sammy's company prints 105 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 105 and 120.
So, LCM of 105 and 120 is 840.

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

Greatest common factors or gcf of 105 and 120 is GCF(105, 120) * LCM(105, 120) = (105 x 120) / GCF(105, 120) = 840.

Find the least number which is exactly divisible by 105 and 120.

Least number which is exactly divisible by 105 and 120 is 840.

Find the LCM of 105 and 120 using GCF method.

Greatest common factor or gcf of 105 and 120 is GCF(105, 120) x LCM(105, 120) = (105 x 120) / GCF(105, 120) = 840.

What is LCM of 105 and 120?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 105 and 120 by Listing Method

Example: Find lcm of 105 and 120 by Listing Method

Steps to find LCM of 105 and 120 by Common Division Method

Example: Find lcm of 105 and 120 by Common Division Method

Steps to find lcm of 105 and 120 by Formula

Example: Find lcm of 105 and 120 by Formula

Examples

What is LCM of 105 and 120?

How to find lcm of two numbers

Definition of LCM

Properties of LCM

Steps to find lcm of 105 and 120 by Listing Method

Example: Find lcm of 105 and 120 by Listing Method

Steps to find LCM of 105 and 120 by Common Division Method

Example: Find lcm of 105 and 120 by Common Division Method

Steps to find lcm of 105 and 120 by Formula

Example: Find lcm of 105 and 120 by Formula

Examples

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