Least Common Multiple of 2200 and 2208

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2200 and 2208 the smallest integer that is 607200 that is divisible by both numbers.

Least Common Multiple (LCM) of 2200 and 2208 is 607200.

LCM(2200,2208) = 607200

LCM of 2200 and 2208

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

LCM of:
and

Least Common Multiple of 2200 and 2208

LCM of 2200 and 2208 is 607200

Least common multiple can be found by multiplying the highest exponent prime factors of 2200 and 2208. First we will calculate the prime factors of 2200 and 2208.

Prime Factorization of 2200


2 2200
2 1100
2 550
5 275
5 55
11 11
1

Prime factors of 2200 are 2, 5,11. Prime factorization of 2200 in exponential form is:

2200 = 23×52×111

Prime Factorization of 2208


2 2208
2 1104
2 552
2 276
2 138
3 69
23 23
1

Prime factors of 2208 are 2, 3,23. Prime factorization of 2208 in exponential form is:

2208 = 25×31×231

Now multiplying the highest exponent prime factors to calculate the LCM of 2200 and 2208.

LCM(2200,2208) = 25×31×52×111×231
LCM(2200,2208) = 607200

Factors of 2200

List of positive integer factors of 2200 that divides 2200 without a remainder.

1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 200, 220, 275, 440, 550, 1100, 2200

Factors of 2208

List of positive integer factors of 2208 that divides 2208 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 69, 92, 96, 138, 184, 276, 368, 552, 736, 1104, 2208

Least Common Multiple of 2200 and 2208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2200 and 2208, than apply into the LCM equation.

GCF(2200,2208) = 8
LCM(2200,2208) = ( 2200 × 2208) / 8
LCM(2200,2208) = 4857600 / 8
LCM(2200,2208) = 607200

Properties of LCM 2200 and 2208

(i) The LCM of 2208 and 2200 is associative

LCM of 2200 and 2208 = LCM of 2208 and 2200

Related Least Common Multiples of 2200

Related Least Common Multiples of 2208

Frequently Asked Questions on LCM of 2200 and 2208

1. What is the LCM of 2200 and 2208?

Answer: LCM of 2200 and 2208 is 607200.

2. What are the Factors of 2200?

Answer: Factors of 2200 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 25, 40, 44, 50, 55, 88, 100, 110, 200, 220, 275, 440, 550, 1100, 2200. There are 24 integers that are factors of 2200. The greatest factor of 2200 is 2200.

3. What are the Factors of 2208?

Answer: Factors of 2208 are 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 69, 92, 96, 138, 184, 276, 368, 552, 736, 1104, 2208. There are 24 integers that are factors of 2208. The greatest factor of 2208 is 2208.

4. How to Find the LCM of 2200 and 2208?

Answer:

Least Common Multiple of 2200 and 2208 = 607200

Step 1: Find the prime factorization of 2200

2200 = 2 x 2 x 2 x 5 x 5 x 11

Step 2: Find the prime factorization of 2208

2208 = 2 x 2 x 2 x 2 x 2 x 3 x 23

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

LCM = 607200 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 11 x 23

Step 4: Therefore, the least common multiple of 2200 and 2208 is 607200.