Least Common Multiple of 2208 and 2214

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2208 and 2214 the smallest integer that is 814752 that is divisible by both numbers.

Least Common Multiple (LCM) of 2208 and 2214 is 814752.

LCM(2208,2214) = 814752

LCM of 2208 and 2214

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

LCM of:
and

Least Common Multiple of 2208 and 2214

LCM of 2208 and 2214 is 814752

Least common multiple can be found by multiplying the highest exponent prime factors of 2208 and 2214. First we will calculate the prime factors of 2208 and 2214.

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

Prime Factorization of 2214


2 2214
3 1107
3 369
3 123
41 41
1

Prime factors of 2214 are 2, 3,41. Prime factorization of 2214 in exponential form is:

2214 = 21×33×411

Now multiplying the highest exponent prime factors to calculate the LCM of 2208 and 2214.

LCM(2208,2214) = 25×33×231×411
LCM(2208,2214) = 814752

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

Factors of 2214

List of positive integer factors of 2214 that divides 2214 without a remainder.

1, 2, 3, 6, 9, 18, 27, 41, 54, 82, 123, 246, 369, 738, 1107, 2214

Least Common Multiple of 2208 and 2214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2208 and 2214, than apply into the LCM equation.

GCF(2208,2214) = 6
LCM(2208,2214) = ( 2208 × 2214) / 6
LCM(2208,2214) = 4888512 / 6
LCM(2208,2214) = 814752

Properties of LCM 2208 and 2214

(i) The LCM of 2214 and 2208 is associative

LCM of 2208 and 2214 = LCM of 2214 and 2208

Related Least Common Multiples of 2208

Related Least Common Multiples of 2214

Frequently Asked Questions on LCM of 2208 and 2214

1. What is the LCM of 2208 and 2214?

Answer: LCM of 2208 and 2214 is 814752.

2. 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.

3. What are the Factors of 2214?

Answer: Factors of 2214 are 1, 2, 3, 6, 9, 18, 27, 41, 54, 82, 123, 246, 369, 738, 1107, 2214. There are 16 integers that are factors of 2214. The greatest factor of 2214 is 2214.

4. How to Find the LCM of 2208 and 2214?

Answer:

Least Common Multiple of 2208 and 2214 = 814752

Step 1: Find the prime factorization of 2208

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

Step 2: Find the prime factorization of 2214

2214 = 2 x 3 x 3 x 3 x 41

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

LCM = 814752 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 23 x 41

Step 4: Therefore, the least common multiple of 2208 and 2214 is 814752.