Least Common Multiple of 2178 and 2184

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2178 and 2184 the smallest integer that is 792792 that is divisible by both numbers.

Least Common Multiple (LCM) of 2178 and 2184 is 792792.

LCM(2178,2184) = 792792

LCM of 2178 and 2184

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 2178 and 2184

LCM of 2178 and 2184 is 792792

Least common multiple can be found by multiplying the highest exponent prime factors of 2178 and 2184. First we will calculate the prime factors of 2178 and 2184.

Prime Factorization of 2178


2 2178
3 1089
3 363
11 121
11 11
1

Prime factors of 2178 are 2, 3,11. Prime factorization of 2178 in exponential form is:

2178 = 21×32×112

Prime Factorization of 2184


2 2184
2 1092
2 546
3 273
7 91
13 13
1

Prime factors of 2184 are 2, 3, 7,13. Prime factorization of 2184 in exponential form is:

2184 = 23×31×71×131

Now multiplying the highest exponent prime factors to calculate the LCM of 2178 and 2184.

LCM(2178,2184) = 23×32×71×112×131
LCM(2178,2184) = 792792

Factors of 2178

List of positive integer factors of 2178 that divides 2178 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 121, 198, 242, 363, 726, 1089, 2178

Factors of 2184

List of positive integer factors of 2184 that divides 2184 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 24, 26, 28, 39, 42, 52, 56, 78, 84, 91, 104, 156, 168, 182, 273, 312, 364, 546, 728, 1092, 2184

Least Common Multiple of 2178 and 2184 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2178 and 2184, than apply into the LCM equation.

GCF(2178,2184) = 6
LCM(2178,2184) = ( 2178 × 2184) / 6
LCM(2178,2184) = 4756752 / 6
LCM(2178,2184) = 792792

Properties of LCM 2178 and 2184

(i) The LCM of 2184 and 2178 is associative

LCM of 2178 and 2184 = LCM of 2184 and 2178

Related Least Common Multiples of 2178

Related Least Common Multiples of 2184

Frequently Asked Questions on LCM of 2178 and 2184

1. What is the LCM of 2178 and 2184?

Answer: LCM of 2178 and 2184 is 792792.

2. What are the Factors of 2178?

Answer: Factors of 2178 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 121, 198, 242, 363, 726, 1089, 2178. There are 18 integers that are factors of 2178. The greatest factor of 2178 is 2178.

3. What are the Factors of 2184?

Answer: Factors of 2184 are 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 24, 26, 28, 39, 42, 52, 56, 78, 84, 91, 104, 156, 168, 182, 273, 312, 364, 546, 728, 1092, 2184. There are 32 integers that are factors of 2184. The greatest factor of 2184 is 2184.

4. How to Find the LCM of 2178 and 2184?

Answer:

Least Common Multiple of 2178 and 2184 = 792792

Step 1: Find the prime factorization of 2178

2178 = 2 x 3 x 3 x 11 x 11

Step 2: Find the prime factorization of 2184

2184 = 2 x 2 x 2 x 3 x 7 x 13

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 792792 = 2 x 2 x 2 x 3 x 3 x 7 x 11 x 11 x 13

Step 4: Therefore, the least common multiple of 2178 and 2184 is 792792.