Least Common Multiple of 216 and 222

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 222 the smallest integer that is 7992 that is divisible by both numbers.

Least Common Multiple (LCM) of 216 and 222 is 7992.

LCM(216,222) = 7992

LCM of 216 and 222

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

LCM of:
and

Least Common Multiple of 216 and 222

LCM of 216 and 222 is 7992

Least common multiple can be found by multiplying the highest exponent prime factors of 216 and 222. First we will calculate the prime factors of 216 and 222.

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 222


2 222
3 111
37 37
1

Prime factors of 222 are 2, 3,37. Prime factorization of 222 in exponential form is:

222 = 21×31×371

Now multiplying the highest exponent prime factors to calculate the LCM of 216 and 222.

LCM(216,222) = 23×33×371
LCM(216,222) = 7992

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 222

List of positive integer factors of 222 that divides 222 without a remainder.

1, 2, 3, 6, 37, 74, 111, 222

Least Common Multiple of 216 and 222 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 222, than apply into the LCM equation.

GCF(216,222) = 6
LCM(216,222) = ( 216 × 222) / 6
LCM(216,222) = 47952 / 6
LCM(216,222) = 7992

Properties of LCM 216 and 222

(i) The LCM of 222 and 216 is associative

LCM of 216 and 222 = LCM of 222 and 216

Related Least Common Multiples of 216

Related Least Common Multiples of 222

Frequently Asked Questions on LCM of 216 and 222

1. What is the LCM of 216 and 222?

Answer: LCM of 216 and 222 is 7992.

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 222?

Answer: Factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222. There are 8 integers that are factors of 222. The greatest factor of 222 is 222.

4. How to Find the LCM of 216 and 222?

Answer:

Least Common Multiple of 216 and 222 = 7992

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 222

222 = 2 x 3 x 37

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

LCM = 7992 = 2 x 2 x 2 x 3 x 3 x 3 x 37

Step 4: Therefore, the least common multiple of 216 and 222 is 7992.