Least Common Multiple of 232 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 232 and 240 the smallest integer that is 6960 that is divisible by both numbers.

Least Common Multiple (LCM) of 232 and 240 is 6960.

LCM(232,240) = 6960

LCM of 232 and 240

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

LCM of:
and

Least Common Multiple of 232 and 240

LCM of 232 and 240 is 6960

Least common multiple can be found by multiplying the highest exponent prime factors of 232 and 240. First we will calculate the prime factors of 232 and 240.

Prime Factorization of 232


2 232
2 116
2 58
29 29
1

Prime factors of 232 are 2,29. Prime factorization of 232 in exponential form is:

232 = 23×291

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 232 and 240.

LCM(232,240) = 24×31×51×291
LCM(232,240) = 6960

Factors of 232

List of positive integer factors of 232 that divides 232 without a remainder.

1, 2, 4, 8, 29, 58, 116, 232

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 232 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 232 and 240, than apply into the LCM equation.

GCF(232,240) = 8
LCM(232,240) = ( 232 × 240) / 8
LCM(232,240) = 55680 / 8
LCM(232,240) = 6960

Properties of LCM 232 and 240

(i) The LCM of 240 and 232 is associative

LCM of 232 and 240 = LCM of 240 and 232

Related Least Common Multiples of 232

Related Least Common Multiples of 240

Frequently Asked Questions on LCM of 232 and 240

1. What is the LCM of 232 and 240?

Answer: LCM of 232 and 240 is 6960.

2. What are the Factors of 232?

Answer: Factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232. There are 8 integers that are factors of 232. The greatest factor of 232 is 232.

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 232 and 240?

Answer:

Least Common Multiple of 232 and 240 = 6960

Step 1: Find the prime factorization of 232

232 = 2 x 2 x 2 x 29

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 = 6960 = 2 x 2 x 2 x 2 x 3 x 5 x 29

Step 4: Therefore, the least common multiple of 232 and 240 is 6960.