Least Common Multiple of 282 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 282 and 289 the smallest integer that is 81498 that is divisible by both numbers.

Least Common Multiple (LCM) of 282 and 289 is 81498.

LCM(282,289) = 81498

LCM of 282 and 289

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

LCM of:
and

Least Common Multiple of 282 and 289

LCM of 282 and 289 is 81498

Least common multiple can be found by multiplying the highest exponent prime factors of 282 and 289. First we will calculate the prime factors of 282 and 289.

Prime Factorization of 282


2 282
3 141
47 47
1

Prime factors of 282 are 2, 3,47. Prime factorization of 282 in exponential form is:

282 = 21×31×471

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 282 and 289.

LCM(282,289) = 21×31×172×471
LCM(282,289) = 81498

Factors of 282

List of positive integer factors of 282 that divides 282 without a remainder.

1, 2, 3, 6, 47, 94, 141, 282

Factors of 289

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

1, 17, 289

Least Common Multiple of 282 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 282 and 289, than apply into the LCM equation.

GCF(282,289) = 1
LCM(282,289) = ( 282 × 289) / 1
LCM(282,289) = 81498 / 1
LCM(282,289) = 81498

Properties of LCM 282 and 289

(i) The LCM of 289 and 282 is associative

LCM of 282 and 289 = LCM of 289 and 282

Related Least Common Multiples of 282

Related Least Common Multiples of 289

Frequently Asked Questions on LCM of 282 and 289

1. What is the LCM of 282 and 289?

Answer: LCM of 282 and 289 is 81498.

2. What are the Factors of 282?

Answer: Factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282. There are 8 integers that are factors of 282. The greatest factor of 282 is 282.

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 282 and 289?

Answer:

Least Common Multiple of 282 and 289 = 81498

Step 1: Find the prime factorization of 282

282 = 2 x 3 x 47

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 = 81498 = 2 x 3 x 17 x 17 x 47

Step 4: Therefore, the least common multiple of 282 and 289 is 81498.