Least Common Multiple of 3200 and 3206

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3200 and 3206 the smallest integer that is 5129600 that is divisible by both numbers.

Least Common Multiple (LCM) of 3200 and 3206 is 5129600.

LCM(3200,3206) = 5129600

LCM of 3200 and 3206

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

LCM of:
and

Least Common Multiple of 3200 and 3206

LCM of 3200 and 3206 is 5129600

Least common multiple can be found by multiplying the highest exponent prime factors of 3200 and 3206. First we will calculate the prime factors of 3200 and 3206.

Prime Factorization of 3200


2 3200
2 1600
2 800
2 400
2 200
2 100
2 50
5 25
5 5
1

Prime factors of 3200 are 2,5. Prime factorization of 3200 in exponential form is:

3200 = 27×52

Prime Factorization of 3206


2 3206
7 1603
229 229
1

Prime factors of 3206 are 2, 7,229. Prime factorization of 3206 in exponential form is:

3206 = 21×71×2291

Now multiplying the highest exponent prime factors to calculate the LCM of 3200 and 3206.

LCM(3200,3206) = 27×52×71×2291
LCM(3200,3206) = 5129600

Factors of 3200

List of positive integer factors of 3200 that divides 3200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200

Factors of 3206

List of positive integer factors of 3206 that divides 3206 without a remainder.

1, 2, 7, 14, 229, 458, 1603, 3206

Least Common Multiple of 3200 and 3206 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3200 and 3206, than apply into the LCM equation.

GCF(3200,3206) = 2
LCM(3200,3206) = ( 3200 × 3206) / 2
LCM(3200,3206) = 10259200 / 2
LCM(3200,3206) = 5129600

Properties of LCM 3200 and 3206

(i) The LCM of 3206 and 3200 is associative

LCM of 3200 and 3206 = LCM of 3206 and 3200

Related Least Common Multiples of 3200

Related Least Common Multiples of 3206

Frequently Asked Questions on LCM of 3200 and 3206

1. What is the LCM of 3200 and 3206?

Answer: LCM of 3200 and 3206 is 5129600.

2. What are the Factors of 3200?

Answer: Factors of 3200 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 128, 160, 200, 320, 400, 640, 800, 1600, 3200. There are 24 integers that are factors of 3200. The greatest factor of 3200 is 3200.

3. What are the Factors of 3206?

Answer: Factors of 3206 are 1, 2, 7, 14, 229, 458, 1603, 3206. There are 8 integers that are factors of 3206. The greatest factor of 3206 is 3206.

4. How to Find the LCM of 3200 and 3206?

Answer:

Least Common Multiple of 3200 and 3206 = 5129600

Step 1: Find the prime factorization of 3200

3200 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 3206

3206 = 2 x 7 x 229

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

LCM = 5129600 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 7 x 229

Step 4: Therefore, the least common multiple of 3200 and 3206 is 5129600.