Least Common Multiple of 1089 and 1092

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1089 and 1092 the smallest integer that is 396396 that is divisible by both numbers.

Least Common Multiple (LCM) of 1089 and 1092 is 396396.

LCM(1089,1092) = 396396

LCM of 1089 and 1092

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

LCM of:
and

Least Common Multiple of 1089 and 1092

LCM of 1089 and 1092 is 396396

Least common multiple can be found by multiplying the highest exponent prime factors of 1089 and 1092. First we will calculate the prime factors of 1089 and 1092.

Prime Factorization of 1089


3 1089
3 363
11 121
11 11
1

Prime factors of 1089 are 3,11. Prime factorization of 1089 in exponential form is:

1089 = 32×112

Prime Factorization of 1092


2 1092
2 546
3 273
7 91
13 13
1

Prime factors of 1092 are 2, 3, 7,13. Prime factorization of 1092 in exponential form is:

1092 = 22×31×71×131

Now multiplying the highest exponent prime factors to calculate the LCM of 1089 and 1092.

LCM(1089,1092) = 22×32×71×112×131
LCM(1089,1092) = 396396

Factors of 1089

List of positive integer factors of 1089 that divides 1089 without a remainder.

1, 3, 9, 11, 33, 99, 121, 363, 1089

Factors of 1092

List of positive integer factors of 1092 that divides 1092 without a remainder.

1, 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, 546, 1092

Least Common Multiple of 1089 and 1092 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1089 and 1092, than apply into the LCM equation.

GCF(1089,1092) = 3
LCM(1089,1092) = ( 1089 × 1092) / 3
LCM(1089,1092) = 1189188 / 3
LCM(1089,1092) = 396396

Properties of LCM 1089 and 1092

(i) The LCM of 1092 and 1089 is associative

LCM of 1089 and 1092 = LCM of 1092 and 1089

Related Least Common Multiples of 1089

Related Least Common Multiples of 1092

Frequently Asked Questions on LCM of 1089 and 1092

1. What is the LCM of 1089 and 1092?

Answer: LCM of 1089 and 1092 is 396396.

2. What are the Factors of 1089?

Answer: Factors of 1089 are 1, 3, 9, 11, 33, 99, 121, 363, 1089. There are 9 integers that are factors of 1089. The greatest factor of 1089 is 1089.

3. What are the Factors of 1092?

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

4. How to Find the LCM of 1089 and 1092?

Answer:

Least Common Multiple of 1089 and 1092 = 396396

Step 1: Find the prime factorization of 1089

1089 = 3 x 3 x 11 x 11

Step 2: Find the prime factorization of 1092

1092 = 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 = 396396 = 2 x 2 x 3 x 3 x 7 x 11 x 11 x 13

Step 4: Therefore, the least common multiple of 1089 and 1092 is 396396.