Least Common Multiple of 217 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 217 and 219 the smallest integer that is 47523 that is divisible by both numbers.

Least Common Multiple (LCM) of 217 and 219 is 47523.

LCM(217,219) = 47523

LCM of 217 and 219

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

LCM of:
and

Least Common Multiple of 217 and 219

LCM of 217 and 219 is 47523

Least common multiple can be found by multiplying the highest exponent prime factors of 217 and 219. First we will calculate the prime factors of 217 and 219.

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

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 217 and 219.

LCM(217,219) = 31×71×311×731
LCM(217,219) = 47523

Factors of 217

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

1, 7, 31, 217

Factors of 219

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

1, 3, 73, 219

Least Common Multiple of 217 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 217 and 219, than apply into the LCM equation.

GCF(217,219) = 1
LCM(217,219) = ( 217 × 219) / 1
LCM(217,219) = 47523 / 1
LCM(217,219) = 47523

Properties of LCM 217 and 219

(i) The LCM of 219 and 217 is associative

LCM of 217 and 219 = LCM of 219 and 217

Related Least Common Multiples of 217

Related Least Common Multiples of 219

Frequently Asked Questions on LCM of 217 and 219

1. What is the LCM of 217 and 219?

Answer: LCM of 217 and 219 is 47523.

2. 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.

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 217 and 219?

Answer:

Least Common Multiple of 217 and 219 = 47523

Step 1: Find the prime factorization of 217

217 = 7 x 31

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 = 47523 = 3 x 7 x 31 x 73

Step 4: Therefore, the least common multiple of 217 and 219 is 47523.