Least Common Multiple of 6864 and 6870

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 6864 and 6870 the smallest integer that is 7859280 that is divisible by both numbers.

Least Common Multiple (LCM) of 6864 and 6870 is 7859280.

LCM(6864,6870) = 7859280

LCM of 6864 and 6870

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

LCM of:
and

Least Common Multiple of 6864 and 6870

LCM of 6864 and 6870 is 7859280

Least common multiple can be found by multiplying the highest exponent prime factors of 6864 and 6870. First we will calculate the prime factors of 6864 and 6870.

Prime Factorization of 6864


2 6864
2 3432
2 1716
2 858
3 429
11 143
13 13
1

Prime factors of 6864 are 2, 3, 11,13. Prime factorization of 6864 in exponential form is:

6864 = 24×31×111×131

Prime Factorization of 6870


2 6870
3 3435
5 1145
229 229
1

Prime factors of 6870 are 2, 3, 5,229. Prime factorization of 6870 in exponential form is:

6870 = 21×31×51×2291

Now multiplying the highest exponent prime factors to calculate the LCM of 6864 and 6870.

LCM(6864,6870) = 24×31×51×111×131×2291
LCM(6864,6870) = 7859280

Factors of 6864

List of positive integer factors of 6864 that divides 6864 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 33, 39, 44, 48, 52, 66, 78, 88, 104, 132, 143, 156, 176, 208, 264, 286, 312, 429, 528, 572, 624, 858, 1144, 1716, 2288, 3432, 6864

Factors of 6870

List of positive integer factors of 6870 that divides 6870 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 229, 458, 687, 1145, 1374, 2290, 3435, 6870

Least Common Multiple of 6864 and 6870 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6864 and 6870, than apply into the LCM equation.

GCF(6864,6870) = 6
LCM(6864,6870) = ( 6864 × 6870) / 6
LCM(6864,6870) = 47155680 / 6
LCM(6864,6870) = 7859280

Properties of LCM 6864 and 6870

(i) The LCM of 6870 and 6864 is associative

LCM of 6864 and 6870 = LCM of 6870 and 6864

Related Least Common Multiples of 6864

Related Least Common Multiples of 6870

Frequently Asked Questions on LCM of 6864 and 6870

1. What is the LCM of 6864 and 6870?

Answer: LCM of 6864 and 6870 is 7859280.

2. What are the Factors of 6864?

Answer: Factors of 6864 are 1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 33, 39, 44, 48, 52, 66, 78, 88, 104, 132, 143, 156, 176, 208, 264, 286, 312, 429, 528, 572, 624, 858, 1144, 1716, 2288, 3432, 6864. There are 40 integers that are factors of 6864. The greatest factor of 6864 is 6864.

3. What are the Factors of 6870?

Answer: Factors of 6870 are 1, 2, 3, 5, 6, 10, 15, 30, 229, 458, 687, 1145, 1374, 2290, 3435, 6870. There are 16 integers that are factors of 6870. The greatest factor of 6870 is 6870.

4. How to Find the LCM of 6864 and 6870?

Answer:

Least Common Multiple of 6864 and 6870 = 7859280

Step 1: Find the prime factorization of 6864

6864 = 2 x 2 x 2 x 2 x 3 x 11 x 13

Step 2: Find the prime factorization of 6870

6870 = 2 x 3 x 5 x 229

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

LCM = 7859280 = 2 x 2 x 2 x 2 x 3 x 5 x 11 x 13 x 229

Step 4: Therefore, the least common multiple of 6864 and 6870 is 7859280.