Least Common Multiple of 289 and 290

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 289 and 290 the smallest integer that is 83810 that is divisible by both numbers.

Least Common Multiple (LCM) of 289 and 290 is 83810.

LCM(289,290) = 83810

LCM of 289 and 290

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

LCM of:
and

Least Common Multiple of 289 and 290

LCM of 289 and 290 is 83810

Least common multiple can be found by multiplying the highest exponent prime factors of 289 and 290. First we will calculate the prime factors of 289 and 290.

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

Prime Factorization of 290


2 290
5 145
29 29
1

Prime factors of 290 are 2, 5,29. Prime factorization of 290 in exponential form is:

290 = 21×51×291

Now multiplying the highest exponent prime factors to calculate the LCM of 289 and 290.

LCM(289,290) = 21×51×172×291
LCM(289,290) = 83810

Factors of 289

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

1, 17, 289

Factors of 290

List of positive integer factors of 290 that divides 290 without a remainder.

1, 2, 5, 10, 29, 58, 145, 290

Least Common Multiple of 289 and 290 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 289 and 290, than apply into the LCM equation.

GCF(289,290) = 1
LCM(289,290) = ( 289 × 290) / 1
LCM(289,290) = 83810 / 1
LCM(289,290) = 83810

Properties of LCM 289 and 290

(i) The LCM of 290 and 289 is associative

LCM of 289 and 290 = LCM of 290 and 289

Related Least Common Multiples of 289

Related Least Common Multiples of 290

Frequently Asked Questions on LCM of 289 and 290

1. What is the LCM of 289 and 290?

Answer: LCM of 289 and 290 is 83810.

2. 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.

3. What are the Factors of 290?

Answer: Factors of 290 are 1, 2, 5, 10, 29, 58, 145, 290. There are 8 integers that are factors of 290. The greatest factor of 290 is 290.

4. How to Find the LCM of 289 and 290?

Answer:

Least Common Multiple of 289 and 290 = 83810

Step 1: Find the prime factorization of 289

289 = 17 x 17

Step 2: Find the prime factorization of 290

290 = 2 x 5 x 29

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

LCM = 83810 = 2 x 5 x 17 x 17 x 29

Step 4: Therefore, the least common multiple of 289 and 290 is 83810.