Least Common Multiple of 216 and 219

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 219 the smallest integer that is 15768 that is divisible by both numbers.

Least Common Multiple (LCM) of 216 and 219 is 15768.

LCM(216,219) = 15768

LCM of 216 and 219

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

LCM of:
and

Least Common Multiple of 216 and 219

LCM of 216 and 219 is 15768

Least common multiple can be found by multiplying the highest exponent prime factors of 216 and 219. First we will calculate the prime factors of 216 and 219.

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 219


3 219
73 73
1

Prime factors of 219 are 3,73. Prime factorization of 219 in exponential form is:

219 = 31×731

Now multiplying the highest exponent prime factors to calculate the LCM of 216 and 219.

LCM(216,219) = 23×33×731
LCM(216,219) = 15768

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 219

List of positive integer factors of 219 that divides 219 without a remainder.

1, 3, 73, 219

Least Common Multiple of 216 and 219 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 219, than apply into the LCM equation.

GCF(216,219) = 3
LCM(216,219) = ( 216 × 219) / 3
LCM(216,219) = 47304 / 3
LCM(216,219) = 15768

Properties of LCM 216 and 219

(i) The LCM of 219 and 216 is associative

LCM of 216 and 219 = LCM of 219 and 216

Related Least Common Multiples of 216

Related Least Common Multiples of 219

Frequently Asked Questions on LCM of 216 and 219

1. What is the LCM of 216 and 219?

Answer: LCM of 216 and 219 is 15768.

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 219?

Answer: Factors of 219 are 1, 3, 73, 219. There are 4 integers that are factors of 219. The greatest factor of 219 is 219.

4. How to Find the LCM of 216 and 219?

Answer:

Least Common Multiple of 216 and 219 = 15768

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 219

219 = 3 x 73

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

LCM = 15768 = 2 x 2 x 2 x 3 x 3 x 3 x 73

Step 4: Therefore, the least common multiple of 216 and 219 is 15768.