Least Common Multiple of 238 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 238 and 240 the smallest integer that is 28560 that is divisible by both numbers.

Least Common Multiple (LCM) of 238 and 240 is 28560.

LCM(238,240) = 28560

LCM of 238 and 240

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

LCM of:
and

Least Common Multiple of 238 and 240

LCM of 238 and 240 is 28560

Least common multiple can be found by multiplying the highest exponent prime factors of 238 and 240. First we will calculate the prime factors of 238 and 240.

Prime Factorization of 238


2 238
7 119
17 17
1

Prime factors of 238 are 2, 7,17. Prime factorization of 238 in exponential form is:

238 = 21×71×171

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 238 and 240.

LCM(238,240) = 24×31×51×71×171
LCM(238,240) = 28560

Factors of 238

List of positive integer factors of 238 that divides 238 without a remainder.

1, 2, 7, 14, 17, 34, 119, 238

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 238 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 238 and 240, than apply into the LCM equation.

GCF(238,240) = 2
LCM(238,240) = ( 238 × 240) / 2
LCM(238,240) = 57120 / 2
LCM(238,240) = 28560

Properties of LCM 238 and 240

(i) The LCM of 240 and 238 is associative

LCM of 238 and 240 = LCM of 240 and 238

Related Least Common Multiples of 238

Related Least Common Multiples of 240

Frequently Asked Questions on LCM of 238 and 240

1. What is the LCM of 238 and 240?

Answer: LCM of 238 and 240 is 28560.

2. What are the Factors of 238?

Answer: Factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238. There are 8 integers that are factors of 238. The greatest factor of 238 is 238.

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 238 and 240?

Answer:

Least Common Multiple of 238 and 240 = 28560

Step 1: Find the prime factorization of 238

238 = 2 x 7 x 17

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 = 28560 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 238 and 240 is 28560.