What is LCM of two numbers?

In mathematics, least common multiple which is commonly known as LCM is defined as the smallest non-zero number which is divisible by both given numbers 306 and 54.

Properties of LCM

  • LCM follows associative property, that means LCM(306, 54) = LCM(54, 306).
  • 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 306 and 54 is 918, where 306 and 54 are less than 918.
  • The LCM of two or more prime numbers is their product.

Steps to find lcm of 306 and 54 by Listing Method

Example: Find lcm of 306 and 54 by Listing Method

  • Multiples of 306: 306, 612, 918, 1224, 1530, 1836, 2142, 2448, 2754, 3060, 3366, 3672, 3978, 4284, 4590, 4896, 5202, 5508, 5814, 6120, 6426, 6732, 7038, 7344, 7650, 7956, 8262, 8568, 8874, 9180, 9486, 9792, 10098, 10404, 10710, 11016, 11322, 11628, 11934, 12240, 12546, 12852, 13158, 13464, 13770, 14076, 14382, 14688, 14994, 15300, 15606, 15912, 16218, 16524
  • Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540, 594, 648, 702, 756, 810, 864, 918, 972, 1026, 1080, 1134, 1188, 1242, 1296, 1350, 1404, 1458, 1512, 1566, 1620, 1674, 1728, 1782, 1836, 1890, 1944, 1998, 2052, 2106, 2160, 2214, 2268, 2322, 2376, 2430, 2484, 2538, 2592, 2646, 2700, 2754, 2808, 2862, 2916, 2970, 3024, 3078, 3132, 3186, 3240, 3294, 3348, 3402, 3456, 3510, 3564, 3618, 3672, 3726, 3780, 3834, 3888, 3942, 3996, 4050, 4104, 4158, 4212, 4266, 4320, 4374, 4428, 4482, 4536, 4590, 4644, 4698, 4752, 4806, 4860, 4914, 4968, 5022, 5076, 5130, 5184, 5238, 5292, 5346, 5400, 5454, 5508, 5562, 5616, 5670, 5724, 5778, 5832, 5886, 5940, 5994, 6048, 6102, 6156, 6210, 6264, 6318, 6372, 6426, 6480, 6534, 6588, 6642, 6696, 6750, 6804, 6858, 6912, 6966, 7020, 7074, 7128, 7182, 7236, 7290, 7344, 7398, 7452, 7506, 7560, 7614, 7668, 7722, 7776, 7830, 7884, 7938, 7992, 8046, 8100, 8154, 8208, 8262, 8316, 8370, 8424, 8478, 8532, 8586, 8640, 8694, 8748, 8802, 8856, 8910, 8964, 9018, 9072, 9126, 9180, 9234, 9288, 9342, 9396, 9450, 9504, 9558, 9612, 9666, 9720, 9774, 9828, 9882, 9936, 9990, 10044, 10098, 10152, 10206, 10260, 10314, 10368, 10422, 10476, 10530, 10584, 10638, 10692, 10746, 10800, 10854, 10908, 10962, 11016, 11070, 11124, 11178, 11232, 11286, 11340, 11394, 11448, 11502, 11556, 11610, 11664, 11718, 11772, 11826, 11880, 11934, 11988, 12042, 12096, 12150, 12204, 12258, 12312, 12366, 12420, 12474, 12528, 12582, 12636, 12690, 12744, 12798, 12852, 12906, 12960, 13014, 13068, 13122, 13176, 13230, 13284, 13338, 13392, 13446, 13500, 13554, 13608, 13662, 13716, 13770, 13824, 13878, 13932, 13986, 14040, 14094, 14148, 14202, 14256, 14310, 14364, 14418, 14472, 14526, 14580, 14634, 14688, 14742, 14796, 14850, 14904, 14958, 15012, 15066, 15120, 15174, 15228, 15282, 15336, 15390, 15444, 15498, 15552, 15606, 15660, 15714, 15768, 15822, 15876, 15930, 15984, 16038, 16092, 16146, 16200, 16254, 16308, 16362, 16416, 16470, 16524

Hence, LCM of 306 and 54 is 918.

Steps to find LCM of 306 and 54 by Common Division Method

Example: Find lcm of 306 and 54 by Common Division Method

2 306 54
3 153 27
3 51 9
3 17 3
17 17 1
1 1

Hence, LCM of 306 and 54 is 2 x 3 x 3 x 3 x 17 = 918.

Steps to find lcm of 306 and 54 by Formula

Example: Find lcm of 306 and 54 by Formula

  • GCF of 306 and 54 = 18
  • LCM of 306 and 54 = (306 x 54) / 18
  • => 16524 / 18

Hence, LCM of 306 and 54 is 918.

Examples

A shopkeeper sells candies in packet of 306 and chocolates in packet of 54. 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 306 and 54.
So, LCM of 306 and 54 is 918.

Both the cricket team and the rugby team had games, today. The cricket team plays every 306 days and the basketball team plays every 54 days. When will both teams have games on the same day again?

Given that the cricket team plays every 306 days and the basketball team plays every 54 days, so for finding the next time when both teams will play again we need to find the LCM of 306 and 54.
So, LCM of 306 and 54 is 918.

Steve spends 306 dollars every day while George spends 54 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 306 and 54.
So, LCM of 306 and 54 is 918.

Sammy's company prints 306 textbooks at a time. Daniel's company prints textbooks in sets of 54 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 306 and 54.
So, LCM of 306 and 54 is 918.

Ariel exercises every 306 days and Rubel every 54 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 306 and 54 is 918.

Find the least common multiple of 306 and 54.

Least common multiple of 306 and 54 is 918.

Find the least number which is exactly divisible by 306 and 54.

Least number which is exactly divisible by 306 and 54 is 918.