Least Common Multiple of 288 and 292

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 288 and 292 the smallest integer that is 21024 that is divisible by both numbers.

Least Common Multiple (LCM) of 288 and 292 is 21024.

LCM(288,292) = 21024

LCM of 288 and 292

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

LCM of:
and

Least Common Multiple of 288 and 292

LCM of 288 and 292 is 21024

Least common multiple can be found by multiplying the highest exponent prime factors of 288 and 292. First we will calculate the prime factors of 288 and 292.

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

Prime Factorization of 292


2 292
2 146
73 73
1

Prime factors of 292 are 2,73. Prime factorization of 292 in exponential form is:

292 = 22×731

Now multiplying the highest exponent prime factors to calculate the LCM of 288 and 292.

LCM(288,292) = 25×32×731
LCM(288,292) = 21024

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

Factors of 292

List of positive integer factors of 292 that divides 292 without a remainder.

1, 2, 4, 73, 146, 292

Least Common Multiple of 288 and 292 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 288 and 292, than apply into the LCM equation.

GCF(288,292) = 4
LCM(288,292) = ( 288 × 292) / 4
LCM(288,292) = 84096 / 4
LCM(288,292) = 21024

Properties of LCM 288 and 292

(i) The LCM of 292 and 288 is associative

LCM of 288 and 292 = LCM of 292 and 288

Related Least Common Multiples of 288

Related Least Common Multiples of 292

Frequently Asked Questions on LCM of 288 and 292

1. What is the LCM of 288 and 292?

Answer: LCM of 288 and 292 is 21024.

2. 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.

3. What are the Factors of 292?

Answer: Factors of 292 are 1, 2, 4, 73, 146, 292. There are 6 integers that are factors of 292. The greatest factor of 292 is 292.

4. How to Find the LCM of 288 and 292?

Answer:

Least Common Multiple of 288 and 292 = 21024

Step 1: Find the prime factorization of 288

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

Step 2: Find the prime factorization of 292

292 = 2 x 2 x 73

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

LCM = 21024 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 73

Step 4: Therefore, the least common multiple of 288 and 292 is 21024.