What is the LCM of 114 and 21 - 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 114 and 21.

Properties of LCM

LCM follows associative property, that means LCM(114, 21) = LCM(21, 114).
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 114 and 21 is 798, where 114 and 21 are less than 798.
The LCM of two or more prime numbers is their product.

Steps to find lcm of 114 and 21 by Listing Method

Find some first multiples of 114 and 21.
Find the least common multiple, and read off the answer!

Example: Find lcm of 114 and 21 by Listing Method

Multiples of 114: 114, 228, 342, 456, 570, 684, 798, 912, 1026, 1140, 1254, 1368, 1482, 1596, 1710, 1824, 1938, 2052, 2166, 2280, 2394
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 462, 483, 504, 525, 546, 567, 588, 609, 630, 651, 672, 693, 714, 735, 756, 777, 798, 819, 840, 861, 882, 903, 924, 945, 966, 987, 1008, 1029, 1050, 1071, 1092, 1113, 1134, 1155, 1176, 1197, 1218, 1239, 1260, 1281, 1302, 1323, 1344, 1365, 1386, 1407, 1428, 1449, 1470, 1491, 1512, 1533, 1554, 1575, 1596, 1617, 1638, 1659, 1680, 1701, 1722, 1743, 1764, 1785, 1806, 1827, 1848, 1869, 1890, 1911, 1932, 1953, 1974, 1995, 2016, 2037, 2058, 2079, 2100, 2121, 2142, 2163, 2184, 2205, 2226, 2247, 2268, 2289, 2310, 2331, 2352, 2373, 2394

Hence, LCM of 114 and 21 is 798.

Steps to find LCM of 114 and 21 by Common Division Method

Find all the prime numbers that would divide 114 and 21 without leaving any remainder.
Multiply the numbers obtained in step 1, and read off the answer!

Example: Find lcm of 114 and 21 by Common Division Method

2	114 21
3	57 21
7	19 7
19	19 1
	1 1

Hence, LCM of 114 and 21 is 2 x 3 x 7 x 19 = 798.

Steps to find lcm of 114 and 21 by Formula

The formula for LCM is LCM (114, 21) = (114 x 21) / GCF (114, 21)
Apply the formula, and read off the answer!

Example: Find lcm of 114 and 21 by Formula

GCF of 114 and 21 = 3
LCM of 114 and 21 = (114 x 21) / 3
=> 2394 / 3

Hence, LCM of 114 and 21 is 798.

Examples

A shopkeeper sells candies in packet of 114 and chocolates in packet of 21. 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 114 and 21.
So, LCM of 114 and 21 is 798.

Both the cricket team and the rugby team had games, today. The cricket team plays every 114 days and the basketball team plays every 21 days. When will both teams have games on the same day again?

Given that the cricket team plays every 114 days and the basketball team plays every 21 days, so for finding the next time when both teams will play again we need to find the LCM of 114 and 21.
So, LCM of 114 and 21 is 798.

Steve spends 114 dollars every day while George spends 21 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 114 and 21.
So, LCM of 114 and 21 is 798.

Sammy's company prints 114 textbooks at a time. Daniel's company prints textbooks in sets of 21 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 114 and 21.
So, LCM of 114 and 21 is 798.

Ariel exercises every 114 days and Rubel every 21 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 114 and 21 is 798.

Find the least common multiple of 114 and 21.

Least common multiple of 114 and 21 is 798.

Find the least number which is exactly divisible by 114 and 21.

Least number which is exactly divisible by 114 and 21 is 798.

What is LCM of 114 and 21?

How to find lcm of two numbers

What is LCM?

Properties of LCM

Steps to find lcm of 114 and 21 by Listing Method

Example: Find lcm of 114 and 21 by Listing Method

Steps to find LCM of 114 and 21 by Common Division Method

Example: Find lcm of 114 and 21 by Common Division Method

Steps to find lcm of 114 and 21 by Formula

Example: Find lcm of 114 and 21 by Formula

Examples

What is LCM of 114 and 21?

How to find lcm of two numbers

What is LCM?

Properties of LCM

Steps to find lcm of 114 and 21 by Listing Method

Example: Find lcm of 114 and 21 by Listing Method

Steps to find LCM of 114 and 21 by Common Division Method

Example: Find lcm of 114 and 21 by Common Division Method

Steps to find lcm of 114 and 21 by Formula

Example: Find lcm of 114 and 21 by Formula

Examples

Recommended

User Also Visited