Least Common Multiple of 286 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 286 and 288 the smallest integer that is 41184 that is divisible by both numbers.

Least Common Multiple (LCM) of 286 and 288 is 41184.

LCM(286,288) = 41184

LCM of 286 and 288

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

LCM of:
and

Least Common Multiple of 286 and 288

LCM of 286 and 288 is 41184

Least common multiple can be found by multiplying the highest exponent prime factors of 286 and 288. First we will calculate the prime factors of 286 and 288.

Prime Factorization of 286


2 286
11 143
13 13
1

Prime factors of 286 are 2, 11,13. Prime factorization of 286 in exponential form is:

286 = 21×111×131

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 286 and 288.

LCM(286,288) = 25×32×111×131
LCM(286,288) = 41184

Factors of 286

List of positive integer factors of 286 that divides 286 without a remainder.

1, 2, 11, 13, 22, 26, 143, 286

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 286 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 286 and 288, than apply into the LCM equation.

GCF(286,288) = 2
LCM(286,288) = ( 286 × 288) / 2
LCM(286,288) = 82368 / 2
LCM(286,288) = 41184

Properties of LCM 286 and 288

(i) The LCM of 288 and 286 is associative

LCM of 286 and 288 = LCM of 288 and 286

Related Least Common Multiples of 286

Related Least Common Multiples of 288

Frequently Asked Questions on LCM of 286 and 288

1. What is the LCM of 286 and 288?

Answer: LCM of 286 and 288 is 41184.

2. What are the Factors of 286?

Answer: Factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286. There are 8 integers that are factors of 286. The greatest factor of 286 is 286.

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 286 and 288?

Answer:

Least Common Multiple of 286 and 288 = 41184

Step 1: Find the prime factorization of 286

286 = 2 x 11 x 13

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 = 41184 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 11 x 13

Step 4: Therefore, the least common multiple of 286 and 288 is 41184.