Least Common Multiple of 864 and 867

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 867 the smallest integer that is 249696 that is divisible by both numbers.

Least Common Multiple (LCM) of 864 and 867 is 249696.

LCM(864,867) = 249696

LCM of 864 and 867

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

LCM of:
and

Least Common Multiple of 864 and 867

LCM of 864 and 867 is 249696

Least common multiple can be found by multiplying the highest exponent prime factors of 864 and 867. First we will calculate the prime factors of 864 and 867.

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 867


3 867
17 289
17 17
1

Prime factors of 867 are 3,17. Prime factorization of 867 in exponential form is:

867 = 31×172

Now multiplying the highest exponent prime factors to calculate the LCM of 864 and 867.

LCM(864,867) = 25×33×172
LCM(864,867) = 249696

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 867

List of positive integer factors of 867 that divides 867 without a remainder.

1, 3, 17, 51, 289, 867

Least Common Multiple of 864 and 867 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 867, than apply into the LCM equation.

GCF(864,867) = 3
LCM(864,867) = ( 864 × 867) / 3
LCM(864,867) = 749088 / 3
LCM(864,867) = 249696

Properties of LCM 864 and 867

(i) The LCM of 867 and 864 is associative

LCM of 864 and 867 = LCM of 867 and 864

Related Least Common Multiples of 864

Related Least Common Multiples of 867

Frequently Asked Questions on LCM of 864 and 867

1. What is the LCM of 864 and 867?

Answer: LCM of 864 and 867 is 249696.

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 867?

Answer: Factors of 867 are 1, 3, 17, 51, 289, 867. There are 6 integers that are factors of 867. The greatest factor of 867 is 867.

4. How to Find the LCM of 864 and 867?

Answer:

Least Common Multiple of 864 and 867 = 249696

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 867

867 = 3 x 17 x 17

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

LCM = 249696 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 17 x 17

Step 4: Therefore, the least common multiple of 864 and 867 is 249696.