Least Common Multiple of 289 and 296

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 296 the smallest integer that is 85544 that is divisible by both numbers.

Least Common Multiple (LCM) of 289 and 296 is 85544.

LCM(289,296) = 85544

LCM of 289 and 296

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

LCM of:
and

Least Common Multiple of 289 and 296

LCM of 289 and 296 is 85544

Least common multiple can be found by multiplying the highest exponent prime factors of 289 and 296. First we will calculate the prime factors of 289 and 296.

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 296


2 296
2 148
2 74
37 37
1

Prime factors of 296 are 2,37. Prime factorization of 296 in exponential form is:

296 = 23×371

Now multiplying the highest exponent prime factors to calculate the LCM of 289 and 296.

LCM(289,296) = 23×172×371
LCM(289,296) = 85544

Factors of 289

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

1, 17, 289

Factors of 296

List of positive integer factors of 296 that divides 296 without a remainder.

1, 2, 4, 8, 37, 74, 148, 296

Least Common Multiple of 289 and 296 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 296, than apply into the LCM equation.

GCF(289,296) = 1
LCM(289,296) = ( 289 × 296) / 1
LCM(289,296) = 85544 / 1
LCM(289,296) = 85544

Properties of LCM 289 and 296

(i) The LCM of 296 and 289 is associative

LCM of 289 and 296 = LCM of 296 and 289

Related Least Common Multiples of 289

Related Least Common Multiples of 296

Frequently Asked Questions on LCM of 289 and 296

1. What is the LCM of 289 and 296?

Answer: LCM of 289 and 296 is 85544.

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 296?

Answer: Factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296. There are 8 integers that are factors of 296. The greatest factor of 296 is 296.

4. How to Find the LCM of 289 and 296?

Answer:

Least Common Multiple of 289 and 296 = 85544

Step 1: Find the prime factorization of 289

289 = 17 x 17

Step 2: Find the prime factorization of 296

296 = 2 x 2 x 2 x 37

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

LCM = 85544 = 2 x 2 x 2 x 17 x 17 x 37

Step 4: Therefore, the least common multiple of 289 and 296 is 85544.