Least Common Multiple of 2200 and 2205

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 2205 the smallest integer that is 970200 that is divisible by both numbers.

Least Common Multiple (LCM) of 2200 and 2205 is 970200.

LCM(2200,2205) = 970200

LCM of 2200 and 2205

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

LCM of:
and

Least Common Multiple of 2200 and 2205

LCM of 2200 and 2205 is 970200

Least common multiple can be found by multiplying the highest exponent prime factors of 2200 and 2205. First we will calculate the prime factors of 2200 and 2205.

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 2205


3 2205
3 735
5 245
7 49
7 7
1

Prime factors of 2205 are 3, 5,7. Prime factorization of 2205 in exponential form is:

2205 = 32×51×72

Now multiplying the highest exponent prime factors to calculate the LCM of 2200 and 2205.

LCM(2200,2205) = 23×32×52×72×111
LCM(2200,2205) = 970200

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 2205

List of positive integer factors of 2205 that divides 2205 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205

Least Common Multiple of 2200 and 2205 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 2205, than apply into the LCM equation.

GCF(2200,2205) = 5
LCM(2200,2205) = ( 2200 × 2205) / 5
LCM(2200,2205) = 4851000 / 5
LCM(2200,2205) = 970200

Properties of LCM 2200 and 2205

(i) The LCM of 2205 and 2200 is associative

LCM of 2200 and 2205 = LCM of 2205 and 2200

Related Least Common Multiples of 2200

Related Least Common Multiples of 2205

Frequently Asked Questions on LCM of 2200 and 2205

1. What is the LCM of 2200 and 2205?

Answer: LCM of 2200 and 2205 is 970200.

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 2205?

Answer: Factors of 2205 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205. There are 18 integers that are factors of 2205. The greatest factor of 2205 is 2205.

4. How to Find the LCM of 2200 and 2205?

Answer:

Least Common Multiple of 2200 and 2205 = 970200

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 2205

2205 = 3 x 3 x 5 x 7 x 7

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

LCM = 970200 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7 x 7 x 11

Step 4: Therefore, the least common multiple of 2200 and 2205 is 970200.