Least Common Multiple of 864 and 870

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 864 and 870 the smallest integer that is 125280 that is divisible by both numbers.

Least Common Multiple (LCM) of 864 and 870 is 125280.

LCM(864,870) = 125280

LCM of 864 and 870

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

LCM of:
and

Least Common Multiple of 864 and 870

LCM of 864 and 870 is 125280

Least common multiple can be found by multiplying the highest exponent prime factors of 864 and 870. First we will calculate the prime factors of 864 and 870.

Prime Factorization of 864


2 864
2 432
2 216
2 108
2 54
3 27
3 9
3 3
1

Prime factors of 864 are 2,3. Prime factorization of 864 in exponential form is:

864 = 25×33

Prime Factorization of 870


2 870
3 435
5 145
29 29
1

Prime factors of 870 are 2, 3, 5,29. Prime factorization of 870 in exponential form is:

870 = 21×31×51×291

Now multiplying the highest exponent prime factors to calculate the LCM of 864 and 870.

LCM(864,870) = 25×33×51×291
LCM(864,870) = 125280

Factors of 864

List of positive integer factors of 864 that divides 864 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864

Factors of 870

List of positive integer factors of 870 that divides 870 without a remainder.

1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870

Least Common Multiple of 864 and 870 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 864 and 870, than apply into the LCM equation.

GCF(864,870) = 6
LCM(864,870) = ( 864 × 870) / 6
LCM(864,870) = 751680 / 6
LCM(864,870) = 125280

Properties of LCM 864 and 870

(i) The LCM of 870 and 864 is associative

LCM of 864 and 870 = LCM of 870 and 864

Related Least Common Multiples of 864

Related Least Common Multiples of 870

Frequently Asked Questions on LCM of 864 and 870

1. What is the LCM of 864 and 870?

Answer: LCM of 864 and 870 is 125280.

2. What are the Factors of 864?

Answer: Factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864. There are 24 integers that are factors of 864. The greatest factor of 864 is 864.

3. What are the Factors of 870?

Answer: Factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870. There are 16 integers that are factors of 870. The greatest factor of 870 is 870.

4. How to Find the LCM of 864 and 870?

Answer:

Least Common Multiple of 864 and 870 = 125280

Step 1: Find the prime factorization of 864

864 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 870

870 = 2 x 3 x 5 x 29

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

LCM = 125280 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 29

Step 4: Therefore, the least common multiple of 864 and 870 is 125280.