Least Common Multiple of 8509 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 8509 and 8512 the smallest integer that is 72428608 that is divisible by both numbers.

Least Common Multiple (LCM) of 8509 and 8512 is 72428608.

LCM(8509,8512) = 72428608

LCM of 8509 and 8512

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

LCM of:
and

Least Common Multiple of 8509 and 8512

LCM of 8509 and 8512 is 72428608

Least common multiple can be found by multiplying the highest exponent prime factors of 8509 and 8512. First we will calculate the prime factors of 8509 and 8512.

Prime Factorization of 8509


67 8509
127 127
1

Prime factors of 8509 are 67,127. Prime factorization of 8509 in exponential form is:

8509 = 671×1271

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 8509 and 8512.

LCM(8509,8512) = 26×71×191×671×1271
LCM(8509,8512) = 72428608

Factors of 8509

List of positive integer factors of 8509 that divides 8509 without a remainder.

1, 67, 127, 8509

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 8509 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 8509 and 8512, than apply into the LCM equation.

GCF(8509,8512) = 1
LCM(8509,8512) = ( 8509 × 8512) / 1
LCM(8509,8512) = 72428608 / 1
LCM(8509,8512) = 72428608

Properties of LCM 8509 and 8512

(i) The LCM of 8512 and 8509 is associative

LCM of 8509 and 8512 = LCM of 8512 and 8509

Related Least Common Multiples of 8509

Related Least Common Multiples of 8512

Frequently Asked Questions on LCM of 8509 and 8512

1. What is the LCM of 8509 and 8512?

Answer: LCM of 8509 and 8512 is 72428608.

2. What are the Factors of 8509?

Answer: Factors of 8509 are 1, 67, 127, 8509. There are 4 integers that are factors of 8509. The greatest factor of 8509 is 8509.

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 8509 and 8512?

Answer:

Least Common Multiple of 8509 and 8512 = 72428608

Step 1: Find the prime factorization of 8509

8509 = 67 x 127

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 = 72428608 = 2 x 2 x 2 x 2 x 2 x 2 x 7 x 19 x 67 x 127

Step 4: Therefore, the least common multiple of 8509 and 8512 is 72428608.