Least Common Multiple of 287 and 288

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 287 and 288 the smallest integer that is 82656 that is divisible by both numbers.

Least Common Multiple (LCM) of 287 and 288 is 82656.

LCM(287,288) = 82656

LCM of 287 and 288

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

LCM of:
and

Least Common Multiple of 287 and 288

LCM of 287 and 288 is 82656

Least common multiple can be found by multiplying the highest exponent prime factors of 287 and 288. First we will calculate the prime factors of 287 and 288.

Prime Factorization of 287


7 287
41 41
1

Prime factors of 287 are 7,41. Prime factorization of 287 in exponential form is:

287 = 71×411

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

Now multiplying the highest exponent prime factors to calculate the LCM of 287 and 288.

LCM(287,288) = 25×32×71×411
LCM(287,288) = 82656

Factors of 287

List of positive integer factors of 287 that divides 287 without a remainder.

1, 7, 41, 287

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

Least Common Multiple of 287 and 288 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 287 and 288, than apply into the LCM equation.

GCF(287,288) = 1
LCM(287,288) = ( 287 × 288) / 1
LCM(287,288) = 82656 / 1
LCM(287,288) = 82656

Properties of LCM 287 and 288

(i) The LCM of 288 and 287 is associative

LCM of 287 and 288 = LCM of 288 and 287

Related Least Common Multiples of 287

Related Least Common Multiples of 288

Frequently Asked Questions on LCM of 287 and 288

1. What is the LCM of 287 and 288?

Answer: LCM of 287 and 288 is 82656.

2. What are the Factors of 287?

Answer: Factors of 287 are 1, 7, 41, 287. There are 4 integers that are factors of 287. The greatest factor of 287 is 287.

3. 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.

4. How to Find the LCM of 287 and 288?

Answer:

Least Common Multiple of 287 and 288 = 82656

Step 1: Find the prime factorization of 287

287 = 7 x 41

Step 2: Find the prime factorization of 288

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

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

LCM = 82656 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 x 41

Step 4: Therefore, the least common multiple of 287 and 288 is 82656.