Least Common Multiple of 8209 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 8209 and 8214 the smallest integer that is 67428726 that is divisible by both numbers.

Least Common Multiple (LCM) of 8209 and 8214 is 67428726.

LCM(8209,8214) = 67428726

LCM of 8209 and 8214

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

LCM of:
and

Least Common Multiple of 8209 and 8214

LCM of 8209 and 8214 is 67428726

Least common multiple can be found by multiplying the highest exponent prime factors of 8209 and 8214. First we will calculate the prime factors of 8209 and 8214.

Prime Factorization of 8209


8209 8209
1

Prime factors of 8209 are 8209. Prime factorization of 8209 in exponential form is:

8209 = 82091

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 8209 and 8214.

LCM(8209,8214) = 21×31×372×82091
LCM(8209,8214) = 67428726

Factors of 8209

List of positive integer factors of 8209 that divides 8209 without a remainder.

1, 8209

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 8209 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 8209 and 8214, than apply into the LCM equation.

GCF(8209,8214) = 1
LCM(8209,8214) = ( 8209 × 8214) / 1
LCM(8209,8214) = 67428726 / 1
LCM(8209,8214) = 67428726

Properties of LCM 8209 and 8214

(i) The LCM of 8214 and 8209 is associative

LCM of 8209 and 8214 = LCM of 8214 and 8209

Related Least Common Multiples of 8209

Related Least Common Multiples of 8214

Frequently Asked Questions on LCM of 8209 and 8214

1. What is the LCM of 8209 and 8214?

Answer: LCM of 8209 and 8214 is 67428726.

2. What are the Factors of 8209?

Answer: Factors of 8209 are 1, 8209. There are 2 integers that are factors of 8209. The greatest factor of 8209 is 8209.

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 8209 and 8214?

Answer:

Least Common Multiple of 8209 and 8214 = 67428726

Step 1: Find the prime factorization of 8209

8209 = 8209

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 = 67428726 = 2 x 3 x 37 x 37 x 8209

Step 4: Therefore, the least common multiple of 8209 and 8214 is 67428726.