Least Common Multiple of 8208 and 8214

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 8208 and 8214 the smallest integer that is 11236752 that is divisible by both numbers.

Least Common Multiple (LCM) of 8208 and 8214 is 11236752.

LCM(8208,8214) = 11236752

LCM of 8208 and 8214

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

LCM of:
and

Least Common Multiple of 8208 and 8214

LCM of 8208 and 8214 is 11236752

Least common multiple can be found by multiplying the highest exponent prime factors of 8208 and 8214. First we will calculate the prime factors of 8208 and 8214.

Prime Factorization of 8208


2 8208
2 4104
2 2052
2 1026
3 513
3 171
3 57
19 19
1

Prime factors of 8208 are 2, 3,19. Prime factorization of 8208 in exponential form is:

8208 = 24×33×191

Prime Factorization of 8214


2 8214
3 4107
37 1369
37 37
1

Prime factors of 8214 are 2, 3,37. Prime factorization of 8214 in exponential form is:

8214 = 21×31×372

Now multiplying the highest exponent prime factors to calculate the LCM of 8208 and 8214.

LCM(8208,8214) = 24×33×191×372
LCM(8208,8214) = 11236752

Factors of 8208

List of positive integer factors of 8208 that divides 8208 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 36, 38, 48, 54, 57, 72, 76, 108, 114, 144, 152, 171, 216, 228, 304, 342, 432, 456, 513, 684, 912, 1026, 1368, 2052, 2736, 4104, 8208

Factors of 8214

List of positive integer factors of 8214 that divides 8214 without a remainder.

1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214

Least Common Multiple of 8208 and 8214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8208 and 8214, than apply into the LCM equation.

GCF(8208,8214) = 6
LCM(8208,8214) = ( 8208 × 8214) / 6
LCM(8208,8214) = 67420512 / 6
LCM(8208,8214) = 11236752

Properties of LCM 8208 and 8214

(i) The LCM of 8214 and 8208 is associative

LCM of 8208 and 8214 = LCM of 8214 and 8208

Related Least Common Multiples of 8208

Related Least Common Multiples of 8214

Frequently Asked Questions on LCM of 8208 and 8214

1. What is the LCM of 8208 and 8214?

Answer: LCM of 8208 and 8214 is 11236752.

2. What are the Factors of 8208?

Answer: Factors of 8208 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 36, 38, 48, 54, 57, 72, 76, 108, 114, 144, 152, 171, 216, 228, 304, 342, 432, 456, 513, 684, 912, 1026, 1368, 2052, 2736, 4104, 8208. There are 40 integers that are factors of 8208. The greatest factor of 8208 is 8208.

3. What are the Factors of 8214?

Answer: Factors of 8214 are 1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214. There are 12 integers that are factors of 8214. The greatest factor of 8214 is 8214.

4. How to Find the LCM of 8208 and 8214?

Answer:

Least Common Multiple of 8208 and 8214 = 11236752

Step 1: Find the prime factorization of 8208

8208 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 19

Step 2: Find the prime factorization of 8214

8214 = 2 x 3 x 37 x 37

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

LCM = 11236752 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 19 x 37 x 37

Step 4: Therefore, the least common multiple of 8208 and 8214 is 11236752.