Least Common Multiple of 284 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 284 and 289 the smallest integer that is 82076 that is divisible by both numbers.

Least Common Multiple (LCM) of 284 and 289 is 82076.

LCM(284,289) = 82076

LCM of 284 and 289

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

LCM of:
and

Least Common Multiple of 284 and 289

LCM of 284 and 289 is 82076

Least common multiple can be found by multiplying the highest exponent prime factors of 284 and 289. First we will calculate the prime factors of 284 and 289.

Prime Factorization of 284


2 284
2 142
71 71
1

Prime factors of 284 are 2,71. Prime factorization of 284 in exponential form is:

284 = 22×711

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 284 and 289.

LCM(284,289) = 22×172×711
LCM(284,289) = 82076

Factors of 284

List of positive integer factors of 284 that divides 284 without a remainder.

1, 2, 4, 71, 142, 284

Factors of 289

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

1, 17, 289

Least Common Multiple of 284 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 284 and 289, than apply into the LCM equation.

GCF(284,289) = 1
LCM(284,289) = ( 284 × 289) / 1
LCM(284,289) = 82076 / 1
LCM(284,289) = 82076

Properties of LCM 284 and 289

(i) The LCM of 289 and 284 is associative

LCM of 284 and 289 = LCM of 289 and 284

Related Least Common Multiples of 284

Related Least Common Multiples of 289

Frequently Asked Questions on LCM of 284 and 289

1. What is the LCM of 284 and 289?

Answer: LCM of 284 and 289 is 82076.

2. What are the Factors of 284?

Answer: Factors of 284 are 1, 2, 4, 71, 142, 284. There are 6 integers that are factors of 284. The greatest factor of 284 is 284.

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 284 and 289?

Answer:

Least Common Multiple of 284 and 289 = 82076

Step 1: Find the prime factorization of 284

284 = 2 x 2 x 71

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 = 82076 = 2 x 2 x 17 x 17 x 71

Step 4: Therefore, the least common multiple of 284 and 289 is 82076.