Least Common Multiple of 288 and 289

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 288 and 289 the smallest integer that is 83232 that is divisible by both numbers.

Least Common Multiple (LCM) of 288 and 289 is 83232.

LCM(288,289) = 83232

LCM of 288 and 289

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

LCM of:
and

Least Common Multiple of 288 and 289

LCM of 288 and 289 is 83232

Least common multiple can be found by multiplying the highest exponent prime factors of 288 and 289. First we will calculate the prime factors of 288 and 289.

Prime Factorization of 288


2 288
2 144
2 72
2 36
2 18
3 9
3 3
1

Prime factors of 288 are 2,3. Prime factorization of 288 in exponential form is:

288 = 25×32

Prime Factorization of 289


17 289
17 17
1

Prime factors of 289 are 17. Prime factorization of 289 in exponential form is:

289 = 172

Now multiplying the highest exponent prime factors to calculate the LCM of 288 and 289.

LCM(288,289) = 25×32×172
LCM(288,289) = 83232

Factors of 288

List of positive integer factors of 288 that divides 288 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

Factors of 289

List of positive integer factors of 289 that divides 289 without a remainder.

1, 17, 289

Least Common Multiple of 288 and 289 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 288 and 289, than apply into the LCM equation.

GCF(288,289) = 1
LCM(288,289) = ( 288 × 289) / 1
LCM(288,289) = 83232 / 1
LCM(288,289) = 83232

Properties of LCM 288 and 289

(i) The LCM of 289 and 288 is associative

LCM of 288 and 289 = LCM of 289 and 288

Related Least Common Multiples of 288

Related Least Common Multiples of 289

Frequently Asked Questions on LCM of 288 and 289

1. What is the LCM of 288 and 289?

Answer: LCM of 288 and 289 is 83232.

2. What are the Factors of 288?

Answer: Factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288. There are 18 integers that are factors of 288. The greatest factor of 288 is 288.

3. What are the Factors of 289?

Answer: Factors of 289 are 1, 17, 289. There are 3 integers that are factors of 289. The greatest factor of 289 is 289.

4. How to Find the LCM of 288 and 289?

Answer:

Least Common Multiple of 288 and 289 = 83232

Step 1: Find the prime factorization of 288

288 = 2 x 2 x 2 x 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 289

289 = 17 x 17

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

LCM = 83232 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 17 x 17

Step 4: Therefore, the least common multiple of 288 and 289 is 83232.