Least Common Multiple of 216 and 217

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 216 and 217 the smallest integer that is 46872 that is divisible by both numbers.

Least Common Multiple (LCM) of 216 and 217 is 46872.

LCM(216,217) = 46872

LCM of 216 and 217

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

LCM of:
and

Least Common Multiple of 216 and 217

LCM of 216 and 217 is 46872

Least common multiple can be found by multiplying the highest exponent prime factors of 216 and 217. First we will calculate the prime factors of 216 and 217.

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

Prime Factorization of 217


7 217
31 31
1

Prime factors of 217 are 7,31. Prime factorization of 217 in exponential form is:

217 = 71×311

Now multiplying the highest exponent prime factors to calculate the LCM of 216 and 217.

LCM(216,217) = 23×33×71×311
LCM(216,217) = 46872

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

Factors of 217

List of positive integer factors of 217 that divides 217 without a remainder.

1, 7, 31, 217

Least Common Multiple of 216 and 217 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 216 and 217, than apply into the LCM equation.

GCF(216,217) = 1
LCM(216,217) = ( 216 × 217) / 1
LCM(216,217) = 46872 / 1
LCM(216,217) = 46872

Properties of LCM 216 and 217

(i) The LCM of 217 and 216 is associative

LCM of 216 and 217 = LCM of 217 and 216

Related Least Common Multiples of 216

Related Least Common Multiples of 217

Frequently Asked Questions on LCM of 216 and 217

1. What is the LCM of 216 and 217?

Answer: LCM of 216 and 217 is 46872.

2. 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.

3. What are the Factors of 217?

Answer: Factors of 217 are 1, 7, 31, 217. There are 4 integers that are factors of 217. The greatest factor of 217 is 217.

4. How to Find the LCM of 216 and 217?

Answer:

Least Common Multiple of 216 and 217 = 46872

Step 1: Find the prime factorization of 216

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

Step 2: Find the prime factorization of 217

217 = 7 x 31

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

LCM = 46872 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 31

Step 4: Therefore, the least common multiple of 216 and 217 is 46872.