Least Common Multiple of 208 and 216

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 216 the smallest integer that is 5616 that is divisible by both numbers.

Least Common Multiple (LCM) of 208 and 216 is 5616.

LCM(208,216) = 5616

LCM of 208 and 216

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

LCM of:
and

Least Common Multiple of 208 and 216

LCM of 208 and 216 is 5616

Least common multiple can be found by multiplying the highest exponent prime factors of 208 and 216. First we will calculate the prime factors of 208 and 216.

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 216


2 216
2 108
2 54
3 27
3 9
3 3
1

Prime factors of 216 are 2,3. Prime factorization of 216 in exponential form is:

216 = 23×33

Now multiplying the highest exponent prime factors to calculate the LCM of 208 and 216.

LCM(208,216) = 24×33×131
LCM(208,216) = 5616

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 216

List of positive integer factors of 216 that divides 216 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

Least Common Multiple of 208 and 216 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 216, than apply into the LCM equation.

GCF(208,216) = 8
LCM(208,216) = ( 208 × 216) / 8
LCM(208,216) = 44928 / 8
LCM(208,216) = 5616

Properties of LCM 208 and 216

(i) The LCM of 216 and 208 is associative

LCM of 208 and 216 = LCM of 216 and 208

Related Least Common Multiples of 208

Related Least Common Multiples of 216

Frequently Asked Questions on LCM of 208 and 216

1. What is the LCM of 208 and 216?

Answer: LCM of 208 and 216 is 5616.

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 216?

Answer: Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216. There are 16 integers that are factors of 216. The greatest factor of 216 is 216.

4. How to Find the LCM of 208 and 216?

Answer:

Least Common Multiple of 208 and 216 = 5616

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 216

216 = 2 x 2 x 2 x 3 x 3 x 3

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

LCM = 5616 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 13

Step 4: Therefore, the least common multiple of 208 and 216 is 5616.