Least Common Multiple of 284 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 284 and 288 the smallest integer that is 20448 that is divisible by both numbers.

Least Common Multiple (LCM) of 284 and 288 is 20448.

LCM(284,288) = 20448

LCM of 284 and 288

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

LCM of:
and

Least Common Multiple of 284 and 288

LCM of 284 and 288 is 20448

Least common multiple can be found by multiplying the highest exponent prime factors of 284 and 288. First we will calculate the prime factors of 284 and 288.

Prime Factorization of 284


2 284
2 142
71 71
1

Prime factors of 284 are 2,71. Prime factorization of 284 in exponential form is:

284 = 22×711

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 284 and 288.

LCM(284,288) = 25×32×711
LCM(284,288) = 20448

Factors of 284

List of positive integer factors of 284 that divides 284 without a remainder.

1, 2, 4, 71, 142, 284

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 284 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 284 and 288, than apply into the LCM equation.

GCF(284,288) = 4
LCM(284,288) = ( 284 × 288) / 4
LCM(284,288) = 81792 / 4
LCM(284,288) = 20448

Properties of LCM 284 and 288

(i) The LCM of 288 and 284 is associative

LCM of 284 and 288 = LCM of 288 and 284

Related Least Common Multiples of 284

Related Least Common Multiples of 288

Frequently Asked Questions on LCM of 284 and 288

1. What is the LCM of 284 and 288?

Answer: LCM of 284 and 288 is 20448.

2. What are the Factors of 284?

Answer: Factors of 284 are 1, 2, 4, 71, 142, 284. There are 6 integers that are factors of 284. The greatest factor of 284 is 284.

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 284 and 288?

Answer:

Least Common Multiple of 284 and 288 = 20448

Step 1: Find the prime factorization of 284

284 = 2 x 2 x 71

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 = 20448 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 71

Step 4: Therefore, the least common multiple of 284 and 288 is 20448.