Least Common Multiple of 8500 and 8505

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 8500 and 8505 the smallest integer that is 14458500 that is divisible by both numbers.

Least Common Multiple (LCM) of 8500 and 8505 is 14458500.

LCM(8500,8505) = 14458500

LCM of 8500 and 8505

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

LCM of:
and

Least Common Multiple of 8500 and 8505

LCM of 8500 and 8505 is 14458500

Least common multiple can be found by multiplying the highest exponent prime factors of 8500 and 8505. First we will calculate the prime factors of 8500 and 8505.

Prime Factorization of 8500


2 8500
2 4250
5 2125
5 425
5 85
17 17
1

Prime factors of 8500 are 2, 5,17. Prime factorization of 8500 in exponential form is:

8500 = 22×53×171

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

Now multiplying the highest exponent prime factors to calculate the LCM of 8500 and 8505.

LCM(8500,8505) = 22×35×53×71×171
LCM(8500,8505) = 14458500

Factors of 8500

List of positive integer factors of 8500 that divides 8500 without a remainder.

1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 125, 170, 250, 340, 425, 500, 850, 1700, 2125, 4250, 8500

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

Least Common Multiple of 8500 and 8505 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8500 and 8505, than apply into the LCM equation.

GCF(8500,8505) = 5
LCM(8500,8505) = ( 8500 × 8505) / 5
LCM(8500,8505) = 72292500 / 5
LCM(8500,8505) = 14458500

Properties of LCM 8500 and 8505

(i) The LCM of 8505 and 8500 is associative

LCM of 8500 and 8505 = LCM of 8505 and 8500

Related Least Common Multiples of 8500

Related Least Common Multiples of 8505

Frequently Asked Questions on LCM of 8500 and 8505

1. What is the LCM of 8500 and 8505?

Answer: LCM of 8500 and 8505 is 14458500.

2. What are the Factors of 8500?

Answer: Factors of 8500 are 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 125, 170, 250, 340, 425, 500, 850, 1700, 2125, 4250, 8500. There are 24 integers that are factors of 8500. The greatest factor of 8500 is 8500.

3. 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.

4. How to Find the LCM of 8500 and 8505?

Answer:

Least Common Multiple of 8500 and 8505 = 14458500

Step 1: Find the prime factorization of 8500

8500 = 2 x 2 x 5 x 5 x 5 x 17

Step 2: Find the prime factorization of 8505

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

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

LCM = 14458500 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 5 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 8500 and 8505 is 14458500.