Least Common Multiple of 860 and 864

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 860 and 864 the smallest integer that is 185760 that is divisible by both numbers.

Least Common Multiple (LCM) of 860 and 864 is 185760.

LCM(860,864) = 185760

LCM of 860 and 864

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

LCM of:
and

Least Common Multiple of 860 and 864

LCM of 860 and 864 is 185760

Least common multiple can be found by multiplying the highest exponent prime factors of 860 and 864. First we will calculate the prime factors of 860 and 864.

Prime Factorization of 860


2 860
2 430
5 215
43 43
1

Prime factors of 860 are 2, 5,43. Prime factorization of 860 in exponential form is:

860 = 22×51×431

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

Now multiplying the highest exponent prime factors to calculate the LCM of 860 and 864.

LCM(860,864) = 25×33×51×431
LCM(860,864) = 185760

Factors of 860

List of positive integer factors of 860 that divides 860 without a remainder.

1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860

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

Least Common Multiple of 860 and 864 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 860 and 864, than apply into the LCM equation.

GCF(860,864) = 4
LCM(860,864) = ( 860 × 864) / 4
LCM(860,864) = 743040 / 4
LCM(860,864) = 185760

Properties of LCM 860 and 864

(i) The LCM of 864 and 860 is associative

LCM of 860 and 864 = LCM of 864 and 860

Related Least Common Multiples of 860

Related Least Common Multiples of 864

Frequently Asked Questions on LCM of 860 and 864

1. What is the LCM of 860 and 864?

Answer: LCM of 860 and 864 is 185760.

2. What are the Factors of 860?

Answer: Factors of 860 are 1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860. There are 12 integers that are factors of 860. The greatest factor of 860 is 860.

3. 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.

4. How to Find the LCM of 860 and 864?

Answer:

Least Common Multiple of 860 and 864 = 185760

Step 1: Find the prime factorization of 860

860 = 2 x 2 x 5 x 43

Step 2: Find the prime factorization of 864

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

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

LCM = 185760 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 43

Step 4: Therefore, the least common multiple of 860 and 864 is 185760.