Least Common Multiple of 288 and 290

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 290 the smallest integer that is 41760 that is divisible by both numbers.

Least Common Multiple (LCM) of 288 and 290 is 41760.

LCM(288,290) = 41760

LCM of 288 and 290

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

LCM of:
and

Least Common Multiple of 288 and 290

LCM of 288 and 290 is 41760

Least common multiple can be found by multiplying the highest exponent prime factors of 288 and 290. First we will calculate the prime factors of 288 and 290.

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 290


2 290
5 145
29 29
1

Prime factors of 290 are 2, 5,29. Prime factorization of 290 in exponential form is:

290 = 21×51×291

Now multiplying the highest exponent prime factors to calculate the LCM of 288 and 290.

LCM(288,290) = 25×32×51×291
LCM(288,290) = 41760

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 290

List of positive integer factors of 290 that divides 290 without a remainder.

1, 2, 5, 10, 29, 58, 145, 290

Least Common Multiple of 288 and 290 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 290, than apply into the LCM equation.

GCF(288,290) = 2
LCM(288,290) = ( 288 × 290) / 2
LCM(288,290) = 83520 / 2
LCM(288,290) = 41760

Properties of LCM 288 and 290

(i) The LCM of 290 and 288 is associative

LCM of 288 and 290 = LCM of 290 and 288

Related Least Common Multiples of 288

Related Least Common Multiples of 290

Frequently Asked Questions on LCM of 288 and 290

1. What is the LCM of 288 and 290?

Answer: LCM of 288 and 290 is 41760.

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 290?

Answer: Factors of 290 are 1, 2, 5, 10, 29, 58, 145, 290. There are 8 integers that are factors of 290. The greatest factor of 290 is 290.

4. How to Find the LCM of 288 and 290?

Answer:

Least Common Multiple of 288 and 290 = 41760

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 290

290 = 2 x 5 x 29

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

LCM = 41760 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 29

Step 4: Therefore, the least common multiple of 288 and 290 is 41760.