Least Common Multiple of 2205 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 2205 and 2208 the smallest integer that is 1622880 that is divisible by both numbers.

Least Common Multiple (LCM) of 2205 and 2208 is 1622880.

LCM(2205,2208) = 1622880

LCM of 2205 and 2208

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

LCM of:
and

Least Common Multiple of 2205 and 2208

LCM of 2205 and 2208 is 1622880

Least common multiple can be found by multiplying the highest exponent prime factors of 2205 and 2208. First we will calculate the prime factors of 2205 and 2208.

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

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 2205 and 2208.

LCM(2205,2208) = 25×32×51×72×231
LCM(2205,2208) = 1622880

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

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 2205 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 2205 and 2208, than apply into the LCM equation.

GCF(2205,2208) = 3
LCM(2205,2208) = ( 2205 × 2208) / 3
LCM(2205,2208) = 4868640 / 3
LCM(2205,2208) = 1622880

Properties of LCM 2205 and 2208

(i) The LCM of 2208 and 2205 is associative

LCM of 2205 and 2208 = LCM of 2208 and 2205

Related Least Common Multiples of 2205

Related Least Common Multiples of 2208

Frequently Asked Questions on LCM of 2205 and 2208

1. What is the LCM of 2205 and 2208?

Answer: LCM of 2205 and 2208 is 1622880.

2. 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.

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 2205 and 2208?

Answer:

Least Common Multiple of 2205 and 2208 = 1622880

Step 1: Find the prime factorization of 2205

2205 = 3 x 3 x 5 x 7 x 7

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 = 1622880 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 7 x 23

Step 4: Therefore, the least common multiple of 2205 and 2208 is 1622880.