Least Common Multiple of 208 and 214

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 208 and 214 the smallest integer that is 22256 that is divisible by both numbers.

Least Common Multiple (LCM) of 208 and 214 is 22256.

LCM(208,214) = 22256

LCM of 208 and 214

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

LCM of:
and

Least Common Multiple of 208 and 214

LCM of 208 and 214 is 22256

Least common multiple can be found by multiplying the highest exponent prime factors of 208 and 214. First we will calculate the prime factors of 208 and 214.

Prime Factorization of 208


2 208
2 104
2 52
2 26
13 13
1

Prime factors of 208 are 2,13. Prime factorization of 208 in exponential form is:

208 = 24×131

Prime Factorization of 214


2 214
107 107
1

Prime factors of 214 are 2,107. Prime factorization of 214 in exponential form is:

214 = 21×1071

Now multiplying the highest exponent prime factors to calculate the LCM of 208 and 214.

LCM(208,214) = 24×131×1071
LCM(208,214) = 22256

Factors of 208

List of positive integer factors of 208 that divides 208 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 208

Factors of 214

List of positive integer factors of 214 that divides 214 without a remainder.

1, 2, 107, 214

Least Common Multiple of 208 and 214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 208 and 214, than apply into the LCM equation.

GCF(208,214) = 2
LCM(208,214) = ( 208 × 214) / 2
LCM(208,214) = 44512 / 2
LCM(208,214) = 22256

Properties of LCM 208 and 214

(i) The LCM of 214 and 208 is associative

LCM of 208 and 214 = LCM of 214 and 208

Related Least Common Multiples of 208

Related Least Common Multiples of 214

Frequently Asked Questions on LCM of 208 and 214

1. What is the LCM of 208 and 214?

Answer: LCM of 208 and 214 is 22256.

2. What are the Factors of 208?

Answer: Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. There are 10 integers that are factors of 208. The greatest factor of 208 is 208.

3. What are the Factors of 214?

Answer: Factors of 214 are 1, 2, 107, 214. There are 4 integers that are factors of 214. The greatest factor of 214 is 214.

4. How to Find the LCM of 208 and 214?

Answer:

Least Common Multiple of 208 and 214 = 22256

Step 1: Find the prime factorization of 208

208 = 2 x 2 x 2 x 2 x 13

Step 2: Find the prime factorization of 214

214 = 2 x 107

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

LCM = 22256 = 2 x 2 x 2 x 2 x 13 x 107

Step 4: Therefore, the least common multiple of 208 and 214 is 22256.