Least Common Multiple of 288 and 294

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 294 the smallest integer that is 14112 that is divisible by both numbers.

Least Common Multiple (LCM) of 288 and 294 is 14112.

LCM(288,294) = 14112

LCM of 288 and 294

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

LCM of:
and

Least Common Multiple of 288 and 294

LCM of 288 and 294 is 14112

Least common multiple can be found by multiplying the highest exponent prime factors of 288 and 294. First we will calculate the prime factors of 288 and 294.

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 294


2 294
3 147
7 49
7 7
1

Prime factors of 294 are 2, 3,7. Prime factorization of 294 in exponential form is:

294 = 21×31×72

Now multiplying the highest exponent prime factors to calculate the LCM of 288 and 294.

LCM(288,294) = 25×32×72
LCM(288,294) = 14112

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 294

List of positive integer factors of 294 that divides 294 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294

Least Common Multiple of 288 and 294 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 294, than apply into the LCM equation.

GCF(288,294) = 6
LCM(288,294) = ( 288 × 294) / 6
LCM(288,294) = 84672 / 6
LCM(288,294) = 14112

Properties of LCM 288 and 294

(i) The LCM of 294 and 288 is associative

LCM of 288 and 294 = LCM of 294 and 288

Related Least Common Multiples of 288

Related Least Common Multiples of 294

Frequently Asked Questions on LCM of 288 and 294

1. What is the LCM of 288 and 294?

Answer: LCM of 288 and 294 is 14112.

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 294?

Answer: Factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294. There are 12 integers that are factors of 294. The greatest factor of 294 is 294.

4. How to Find the LCM of 288 and 294?

Answer:

Least Common Multiple of 288 and 294 = 14112

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 294

294 = 2 x 3 x 7 x 7

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

LCM = 14112 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 x 7

Step 4: Therefore, the least common multiple of 288 and 294 is 14112.