Least Common Multiple of 8505 and 8512

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 8505 and 8512 the smallest integer that is 10342080 that is divisible by both numbers.

Least Common Multiple (LCM) of 8505 and 8512 is 10342080.

LCM(8505,8512) = 10342080

LCM of 8505 and 8512

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

LCM of:
and

Least Common Multiple of 8505 and 8512

LCM of 8505 and 8512 is 10342080

Least common multiple can be found by multiplying the highest exponent prime factors of 8505 and 8512. First we will calculate the prime factors of 8505 and 8512.

Prime Factorization of 8505


3 8505
3 2835
3 945
3 315
3 105
5 35
7 7
1

Prime factors of 8505 are 3, 5,7. Prime factorization of 8505 in exponential form is:

8505 = 35×51×71

Prime Factorization of 8512


2 8512
2 4256
2 2128
2 1064
2 532
2 266
7 133
19 19
1

Prime factors of 8512 are 2, 7,19. Prime factorization of 8512 in exponential form is:

8512 = 26×71×191

Now multiplying the highest exponent prime factors to calculate the LCM of 8505 and 8512.

LCM(8505,8512) = 26×35×51×71×191
LCM(8505,8512) = 10342080

Factors of 8505

List of positive integer factors of 8505 that divides 8505 without a remainder.

1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 81, 105, 135, 189, 243, 315, 405, 567, 945, 1215, 1701, 2835, 8505

Factors of 8512

List of positive integer factors of 8512 that divides 8512 without a remainder.

1, 2, 4, 7, 8, 14, 16, 19, 28, 32, 38, 56, 64, 76, 112, 133, 152, 224, 266, 304, 448, 532, 608, 1064, 1216, 2128, 4256, 8512

Least Common Multiple of 8505 and 8512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8505 and 8512, than apply into the LCM equation.

GCF(8505,8512) = 7
LCM(8505,8512) = ( 8505 × 8512) / 7
LCM(8505,8512) = 72394560 / 7
LCM(8505,8512) = 10342080

Properties of LCM 8505 and 8512

(i) The LCM of 8512 and 8505 is associative

LCM of 8505 and 8512 = LCM of 8512 and 8505

Related Least Common Multiples of 8505

Related Least Common Multiples of 8512

Frequently Asked Questions on LCM of 8505 and 8512

1. What is the LCM of 8505 and 8512?

Answer: LCM of 8505 and 8512 is 10342080.

2. What are the Factors of 8505?

Answer: Factors of 8505 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 81, 105, 135, 189, 243, 315, 405, 567, 945, 1215, 1701, 2835, 8505. There are 24 integers that are factors of 8505. The greatest factor of 8505 is 8505.

3. What are the Factors of 8512?

Answer: Factors of 8512 are 1, 2, 4, 7, 8, 14, 16, 19, 28, 32, 38, 56, 64, 76, 112, 133, 152, 224, 266, 304, 448, 532, 608, 1064, 1216, 2128, 4256, 8512. There are 28 integers that are factors of 8512. The greatest factor of 8512 is 8512.

4. How to Find the LCM of 8505 and 8512?

Answer:

Least Common Multiple of 8505 and 8512 = 10342080

Step 1: Find the prime factorization of 8505

8505 = 3 x 3 x 3 x 3 x 3 x 5 x 7

Step 2: Find the prime factorization of 8512

8512 = 2 x 2 x 2 x 2 x 2 x 2 x 7 x 19

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

LCM = 10342080 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 7 x 19

Step 4: Therefore, the least common multiple of 8505 and 8512 is 10342080.