Least Common Multiple of 240 and 243

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 240 and 243 the smallest integer that is 19440 that is divisible by both numbers.

Least Common Multiple (LCM) of 240 and 243 is 19440.

LCM(240,243) = 19440

LCM of 240 and 243

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

LCM of:
and

Least Common Multiple of 240 and 243

LCM of 240 and 243 is 19440

Least common multiple can be found by multiplying the highest exponent prime factors of 240 and 243. First we will calculate the prime factors of 240 and 243.

Prime Factorization of 240


2 240
2 120
2 60
2 30
3 15
5 5
1

Prime factors of 240 are 2, 3,5. Prime factorization of 240 in exponential form is:

240 = 24×31×51

Prime Factorization of 243


3 243
3 81
3 27
3 9
3 3
1

Prime factors of 243 are 3. Prime factorization of 243 in exponential form is:

243 = 35

Now multiplying the highest exponent prime factors to calculate the LCM of 240 and 243.

LCM(240,243) = 24×35×51
LCM(240,243) = 19440

Factors of 240

List of positive integer factors of 240 that divides 240 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240

Factors of 243

List of positive integer factors of 243 that divides 243 without a remainder.

1, 3, 9, 27, 81, 243

Least Common Multiple of 240 and 243 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 240 and 243, than apply into the LCM equation.

GCF(240,243) = 3
LCM(240,243) = ( 240 × 243) / 3
LCM(240,243) = 58320 / 3
LCM(240,243) = 19440

Properties of LCM 240 and 243

(i) The LCM of 243 and 240 is associative

LCM of 240 and 243 = LCM of 243 and 240

Related Least Common Multiples of 240

Related Least Common Multiples of 243

Frequently Asked Questions on LCM of 240 and 243

1. What is the LCM of 240 and 243?

Answer: LCM of 240 and 243 is 19440.

2. What are the Factors of 240?

Answer: Factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240. There are 20 integers that are factors of 240. The greatest factor of 240 is 240.

3. What are the Factors of 243?

Answer: Factors of 243 are 1, 3, 9, 27, 81, 243. There are 6 integers that are factors of 243. The greatest factor of 243 is 243.

4. How to Find the LCM of 240 and 243?

Answer:

Least Common Multiple of 240 and 243 = 19440

Step 1: Find the prime factorization of 240

240 = 2 x 2 x 2 x 2 x 3 x 5

Step 2: Find the prime factorization of 243

243 = 3 x 3 x 3 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 = 19440 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 240 and 243 is 19440.