Least Common Multiple of 239 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 239 and 240 the smallest integer that is 57360 that is divisible by both numbers.

Least Common Multiple (LCM) of 239 and 240 is 57360.

LCM(239,240) = 57360

LCM of 239 and 240

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

LCM of:
and

Least Common Multiple of 239 and 240

LCM of 239 and 240 is 57360

Least common multiple can be found by multiplying the highest exponent prime factors of 239 and 240. First we will calculate the prime factors of 239 and 240.

Prime Factorization of 239


239 239
1

Prime factors of 239 are 239. Prime factorization of 239 in exponential form is:

239 = 2391

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 239 and 240.

LCM(239,240) = 24×31×51×2391
LCM(239,240) = 57360

Factors of 239

List of positive integer factors of 239 that divides 239 without a remainder.

1, 239

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 239 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 239 and 240, than apply into the LCM equation.

GCF(239,240) = 1
LCM(239,240) = ( 239 × 240) / 1
LCM(239,240) = 57360 / 1
LCM(239,240) = 57360

Properties of LCM 239 and 240

(i) The LCM of 240 and 239 is associative

LCM of 239 and 240 = LCM of 240 and 239

Related Least Common Multiples of 239

Related Least Common Multiples of 240

Frequently Asked Questions on LCM of 239 and 240

1. What is the LCM of 239 and 240?

Answer: LCM of 239 and 240 is 57360.

2. What are the Factors of 239?

Answer: Factors of 239 are 1, 239. There are 2 integers that are factors of 239. The greatest factor of 239 is 239.

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 239 and 240?

Answer:

Least Common Multiple of 239 and 240 = 57360

Step 1: Find the prime factorization of 239

239 = 239

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 = 57360 = 2 x 2 x 2 x 2 x 3 x 5 x 239

Step 4: Therefore, the least common multiple of 239 and 240 is 57360.