Least Common Multiple of 234 and 240

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 234 and 240 the smallest integer that is 9360 that is divisible by both numbers.

Least Common Multiple (LCM) of 234 and 240 is 9360.

LCM(234,240) = 9360

LCM of 234 and 240

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

LCM of:
and

Least Common Multiple of 234 and 240

LCM of 234 and 240 is 9360

Least common multiple can be found by multiplying the highest exponent prime factors of 234 and 240. First we will calculate the prime factors of 234 and 240.

Prime Factorization of 234


2 234
3 117
3 39
13 13
1

Prime factors of 234 are 2, 3,13. Prime factorization of 234 in exponential form is:

234 = 21×32×131

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

Now multiplying the highest exponent prime factors to calculate the LCM of 234 and 240.

LCM(234,240) = 24×32×51×131
LCM(234,240) = 9360

Factors of 234

List of positive integer factors of 234 that divides 234 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234

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

Least Common Multiple of 234 and 240 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 234 and 240, than apply into the LCM equation.

GCF(234,240) = 6
LCM(234,240) = ( 234 × 240) / 6
LCM(234,240) = 56160 / 6
LCM(234,240) = 9360

Properties of LCM 234 and 240

(i) The LCM of 240 and 234 is associative

LCM of 234 and 240 = LCM of 240 and 234

Related Least Common Multiples of 234

Related Least Common Multiples of 240

Frequently Asked Questions on LCM of 234 and 240

1. What is the LCM of 234 and 240?

Answer: LCM of 234 and 240 is 9360.

2. What are the Factors of 234?

Answer: Factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234. There are 12 integers that are factors of 234. The greatest factor of 234 is 234.

3. 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.

4. How to Find the LCM of 234 and 240?

Answer:

Least Common Multiple of 234 and 240 = 9360

Step 1: Find the prime factorization of 234

234 = 2 x 3 x 3 x 13

Step 2: Find the prime factorization of 240

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

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

LCM = 9360 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 234 and 240 is 9360.