What is the LCM of 18 and 360 - Find out answer step by step

What does LCM mean in mathematics?

The least common multiple or LCM of two numbers 18 and 360 is defined as the smallest positive integer which is divisible by both of them. It is represented by LCM(18, 360).

Properties of LCM

LCM follows associative property, that means LCM(18, 360) = LCM(360, 18).
LCM follows commutative property, which means LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c)).
LCM follows distributive property, which means LCM(ab, bc, ad) = d * LCM(x, y, z).
The LCM of two given numbers is never less than any of those numbers. Eg- LCM of 18 and 360 is 360, where 18 and 360 are less than 360.
The LCM of two or more prime numbers is their product.

Steps to find lcm of 18 and 360 by Listing Method

Find some first multiples of 18 and 360.
Find the least common multiple, and read off the answer!

Example: Find lcm of 18 and 360 by Listing Method

Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270, 288, 306, 324, 342, 360, 378, 396, 414, 432, 450, 468, 486, 504, 522, 540, 558, 576, 594, 612, 630, 648, 666, 684, 702, 720, 738, 756, 774, 792, 810, 828, 846, 864, 882, 900, 918, 936, 954, 972, 990, 1008, 1026, 1044, 1062, 1080, 1098, 1116, 1134, 1152, 1170, 1188, 1206, 1224, 1242, 1260, 1278, 1296, 1314, 1332, 1350, 1368, 1386, 1404, 1422, 1440, 1458, 1476, 1494, 1512, 1530, 1548, 1566, 1584, 1602, 1620, 1638, 1656, 1674, 1692, 1710, 1728, 1746, 1764, 1782, 1800, 1818, 1836, 1854, 1872, 1890, 1908, 1926, 1944, 1962, 1980, 1998, 2016, 2034, 2052, 2070, 2088, 2106, 2124, 2142, 2160, 2178, 2196, 2214, 2232, 2250, 2268, 2286, 2304, 2322, 2340, 2358, 2376, 2394, 2412, 2430, 2448, 2466, 2484, 2502, 2520, 2538, 2556, 2574, 2592, 2610, 2628, 2646, 2664, 2682, 2700, 2718, 2736, 2754, 2772, 2790, 2808, 2826, 2844, 2862, 2880, 2898, 2916, 2934, 2952, 2970, 2988, 3006, 3024, 3042, 3060, 3078, 3096, 3114, 3132, 3150, 3168, 3186, 3204, 3222, 3240, 3258, 3276, 3294, 3312, 3330, 3348, 3366, 3384, 3402, 3420, 3438, 3456, 3474, 3492, 3510, 3528, 3546, 3564, 3582, 3600, 3618, 3636, 3654, 3672, 3690, 3708, 3726, 3744, 3762, 3780, 3798, 3816, 3834, 3852, 3870, 3888, 3906, 3924, 3942, 3960, 3978, 3996, 4014, 4032, 4050, 4068, 4086, 4104, 4122, 4140, 4158, 4176, 4194, 4212, 4230, 4248, 4266, 4284, 4302, 4320, 4338, 4356, 4374, 4392, 4410, 4428, 4446, 4464, 4482, 4500, 4518, 4536, 4554, 4572, 4590, 4608, 4626, 4644, 4662, 4680, 4698, 4716, 4734, 4752, 4770, 4788, 4806, 4824, 4842, 4860, 4878, 4896, 4914, 4932, 4950, 4968, 4986, 5004, 5022, 5040, 5058, 5076, 5094, 5112, 5130, 5148, 5166, 5184, 5202, 5220, 5238, 5256, 5274, 5292, 5310, 5328, 5346, 5364, 5382, 5400, 5418, 5436, 5454, 5472, 5490, 5508, 5526, 5544, 5562, 5580, 5598, 5616, 5634, 5652, 5670, 5688, 5706, 5724, 5742, 5760, 5778, 5796, 5814, 5832, 5850, 5868, 5886, 5904, 5922, 5940, 5958, 5976, 5994, 6012, 6030, 6048, 6066, 6084, 6102, 6120, 6138, 6156, 6174, 6192, 6210, 6228, 6246, 6264, 6282, 6300, 6318, 6336, 6354, 6372, 6390, 6408, 6426, 6444, 6462, 6480
Multiples of 360: 360, 720, 1080, 1440, 1800, 2160, 2520, 2880, 3240, 3600, 3960, 4320, 4680, 5040, 5400, 5760, 6120, 6480

Hence, LCM of 18 and 360 is 360.

Steps to find LCM of 18 and 360 by Common Division Method

Find all the prime numbers that would divide 18 and 360 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 18 and 360 by Common Division Method

2	18 360
2	9 180
2	9 90
3	9 45
3	3 15
5	1 5
	1 1

Hence, LCM of 18 and 360 is 2 x 2 x 2 x 3 x 3 x 5 = 360.

Steps to find lcm of 18 and 360 by Formula

The formula for LCM is LCM (18, 360) = (18 x 360) / GCF (18, 360)
Apply the formula, and read off the answer!

Example: Find lcm of 18 and 360 by Formula

GCF of 18 and 360 = 18
LCM of 18 and 360 = (18 x 360) / 18
=> 6480 / 18

Hence, LCM of 18 and 360 is 360.

Examples

A shopkeeper sells candies in packet of 18 and chocolates in packet of 360. 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 18 and 360.
So, LCM of 18 and 360 is 360.

Both the cricket team and the rugby team had games, today. The cricket team plays every 18 days and the basketball team plays every 360 days. When will both teams have games on the same day again?

Given that the cricket team plays every 18 days and the basketball team plays every 360 days, so for finding the next time when both teams will play again we need to find the LCM of 18 and 360.
So, LCM of 18 and 360 is 360.

Steve spends 18 dollars every day while George spends 360 dollars every day. What is the least number of days it will take each person to spend the same amount of money?

To find the least number of days that would be taken to be able to spend the same amount of dollars we need to find the LCM of 18 and 360.
So, LCM of 18 and 360 is 360.

Sammy's company prints 18 textbooks at a time. Daniel's company prints textbooks in sets of 360 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 18 and 360.
So, LCM of 18 and 360 is 360.

Ariel exercises every 18 days and Rubel every 360 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 18 and 360 is 360.

Find the least common multiple of 18 and 360.

Least common multiple of 18 and 360 is 360.

Find the least number which is exactly divisible by 18 and 360.

Least number which is exactly divisible by 18 and 360 is 360.

What is LCM of 18 and 360?

How to find lcm of two numbers

What does LCM mean in mathematics?

Properties of LCM

Steps to find lcm of 18 and 360 by Listing Method

Example: Find lcm of 18 and 360 by Listing Method

Steps to find LCM of 18 and 360 by Common Division Method

Example: Find lcm of 18 and 360 by Common Division Method

Steps to find lcm of 18 and 360 by Formula

Example: Find lcm of 18 and 360 by Formula

Examples

What is LCM of 18 and 360?

How to find lcm of two numbers

What does LCM mean in mathematics?

Properties of LCM

Steps to find lcm of 18 and 360 by Listing Method

Example: Find lcm of 18 and 360 by Listing Method

Steps to find LCM of 18 and 360 by Common Division Method

Example: Find lcm of 18 and 360 by Common Division Method

Steps to find lcm of 18 and 360 by Formula

Example: Find lcm of 18 and 360 by Formula

Examples

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