Least Common Multiple of 209 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 209 and 216 the smallest integer that is 45144 that is divisible by both numbers.

Least Common Multiple (LCM) of 209 and 216 is 45144.

LCM(209,216) = 45144

LCM of 209 and 216

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

LCM of:
and

Least Common Multiple of 209 and 216

LCM of 209 and 216 is 45144

Least common multiple can be found by multiplying the highest exponent prime factors of 209 and 216. First we will calculate the prime factors of 209 and 216.

Prime Factorization of 209


11 209
19 19
1

Prime factors of 209 are 11,19. Prime factorization of 209 in exponential form is:

209 = 111×191

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 209 and 216.

LCM(209,216) = 23×33×111×191
LCM(209,216) = 45144

Factors of 209

List of positive integer factors of 209 that divides 209 without a remainder.

1, 11, 19, 209

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 209 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 209 and 216, than apply into the LCM equation.

GCF(209,216) = 1
LCM(209,216) = ( 209 × 216) / 1
LCM(209,216) = 45144 / 1
LCM(209,216) = 45144

Properties of LCM 209 and 216

(i) The LCM of 216 and 209 is associative

LCM of 209 and 216 = LCM of 216 and 209

Related Least Common Multiples of 209

Related Least Common Multiples of 216

Frequently Asked Questions on LCM of 209 and 216

1. What is the LCM of 209 and 216?

Answer: LCM of 209 and 216 is 45144.

2. What are the Factors of 209?

Answer: Factors of 209 are 1, 11, 19, 209. There are 4 integers that are factors of 209. The greatest factor of 209 is 209.

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 209 and 216?

Answer:

Least Common Multiple of 209 and 216 = 45144

Step 1: Find the prime factorization of 209

209 = 11 x 19

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 = 45144 = 2 x 2 x 2 x 3 x 3 x 3 x 11 x 19

Step 4: Therefore, the least common multiple of 209 and 216 is 45144.