Least Common Multiple of 282 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 282 and 288 the smallest integer that is 13536 that is divisible by both numbers.

Least Common Multiple (LCM) of 282 and 288 is 13536.

LCM(282,288) = 13536

LCM of 282 and 288

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

LCM of:
and

Least Common Multiple of 282 and 288

LCM of 282 and 288 is 13536

Least common multiple can be found by multiplying the highest exponent prime factors of 282 and 288. First we will calculate the prime factors of 282 and 288.

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 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 282 and 288.

LCM(282,288) = 25×32×471
LCM(282,288) = 13536

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 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 282 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 282 and 288, than apply into the LCM equation.

GCF(282,288) = 6
LCM(282,288) = ( 282 × 288) / 6
LCM(282,288) = 81216 / 6
LCM(282,288) = 13536

Properties of LCM 282 and 288

(i) The LCM of 288 and 282 is associative

LCM of 282 and 288 = LCM of 288 and 282

Related Least Common Multiples of 282

Related Least Common Multiples of 288

Frequently Asked Questions on LCM of 282 and 288

1. What is the LCM of 282 and 288?

Answer: LCM of 282 and 288 is 13536.

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 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 282 and 288?

Answer:

Least Common Multiple of 282 and 288 = 13536

Step 1: Find the prime factorization of 282

282 = 2 x 3 x 47

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 = 13536 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 47

Step 4: Therefore, the least common multiple of 282 and 288 is 13536.