Least Common Multiple of 208 and 212

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 212 the smallest integer that is 11024 that is divisible by both numbers.

Least Common Multiple (LCM) of 208 and 212 is 11024.

LCM(208,212) = 11024

LCM of 208 and 212

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

LCM of:
and

Least Common Multiple of 208 and 212

LCM of 208 and 212 is 11024

Least common multiple can be found by multiplying the highest exponent prime factors of 208 and 212. First we will calculate the prime factors of 208 and 212.

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 212


2 212
2 106
53 53
1

Prime factors of 212 are 2,53. Prime factorization of 212 in exponential form is:

212 = 22×531

Now multiplying the highest exponent prime factors to calculate the LCM of 208 and 212.

LCM(208,212) = 24×131×531
LCM(208,212) = 11024

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 212

List of positive integer factors of 212 that divides 212 without a remainder.

1, 2, 4, 53, 106, 212

Least Common Multiple of 208 and 212 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 212, than apply into the LCM equation.

GCF(208,212) = 4
LCM(208,212) = ( 208 × 212) / 4
LCM(208,212) = 44096 / 4
LCM(208,212) = 11024

Properties of LCM 208 and 212

(i) The LCM of 212 and 208 is associative

LCM of 208 and 212 = LCM of 212 and 208

Related Least Common Multiples of 208

Related Least Common Multiples of 212

Frequently Asked Questions on LCM of 208 and 212

1. What is the LCM of 208 and 212?

Answer: LCM of 208 and 212 is 11024.

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 212?

Answer: Factors of 212 are 1, 2, 4, 53, 106, 212. There are 6 integers that are factors of 212. The greatest factor of 212 is 212.

4. How to Find the LCM of 208 and 212?

Answer:

Least Common Multiple of 208 and 212 = 11024

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 212

212 = 2 x 2 x 53

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

LCM = 11024 = 2 x 2 x 2 x 2 x 13 x 53

Step 4: Therefore, the least common multiple of 208 and 212 is 11024.