Least Common Multiple of 213 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 213 and 217 the smallest integer that is 46221 that is divisible by both numbers.

Least Common Multiple (LCM) of 213 and 217 is 46221.

LCM(213,217) = 46221

LCM of 213 and 217

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

LCM of:
and

Least Common Multiple of 213 and 217

LCM of 213 and 217 is 46221

Least common multiple can be found by multiplying the highest exponent prime factors of 213 and 217. First we will calculate the prime factors of 213 and 217.

Prime Factorization of 213


3 213
71 71
1

Prime factors of 213 are 3,71. Prime factorization of 213 in exponential form is:

213 = 31×711

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 213 and 217.

LCM(213,217) = 31×71×311×711
LCM(213,217) = 46221

Factors of 213

List of positive integer factors of 213 that divides 213 without a remainder.

1, 3, 71, 213

Factors of 217

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

1, 7, 31, 217

Least Common Multiple of 213 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 213 and 217, than apply into the LCM equation.

GCF(213,217) = 1
LCM(213,217) = ( 213 × 217) / 1
LCM(213,217) = 46221 / 1
LCM(213,217) = 46221

Properties of LCM 213 and 217

(i) The LCM of 217 and 213 is associative

LCM of 213 and 217 = LCM of 217 and 213

Related Least Common Multiples of 213

Related Least Common Multiples of 217

Frequently Asked Questions on LCM of 213 and 217

1. What is the LCM of 213 and 217?

Answer: LCM of 213 and 217 is 46221.

2. What are the Factors of 213?

Answer: Factors of 213 are 1, 3, 71, 213. There are 4 integers that are factors of 213. The greatest factor of 213 is 213.

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 213 and 217?

Answer:

Least Common Multiple of 213 and 217 = 46221

Step 1: Find the prime factorization of 213

213 = 3 x 71

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 = 46221 = 3 x 7 x 31 x 71

Step 4: Therefore, the least common multiple of 213 and 217 is 46221.