Least Common Multiple of 212 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 212 and 217 the smallest integer that is 46004 that is divisible by both numbers.

Least Common Multiple (LCM) of 212 and 217 is 46004.

LCM(212,217) = 46004

LCM of 212 and 217

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

LCM of:
and

Least Common Multiple of 212 and 217

LCM of 212 and 217 is 46004

Least common multiple can be found by multiplying the highest exponent prime factors of 212 and 217. First we will calculate the prime factors of 212 and 217.

Prime Factorization of 212


2 212
2 106
53 53
1

Prime factors of 212 are 2,53. Prime factorization of 212 in exponential form is:

212 = 22×531

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 212 and 217.

LCM(212,217) = 22×71×311×531
LCM(212,217) = 46004

Factors of 212

List of positive integer factors of 212 that divides 212 without a remainder.

1, 2, 4, 53, 106, 212

Factors of 217

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

1, 7, 31, 217

Least Common Multiple of 212 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 212 and 217, than apply into the LCM equation.

GCF(212,217) = 1
LCM(212,217) = ( 212 × 217) / 1
LCM(212,217) = 46004 / 1
LCM(212,217) = 46004

Properties of LCM 212 and 217

(i) The LCM of 217 and 212 is associative

LCM of 212 and 217 = LCM of 217 and 212

Related Least Common Multiples of 212

Related Least Common Multiples of 217

Frequently Asked Questions on LCM of 212 and 217

1. What is the LCM of 212 and 217?

Answer: LCM of 212 and 217 is 46004.

2. What are the Factors of 212?

Answer: Factors of 212 are 1, 2, 4, 53, 106, 212. There are 6 integers that are factors of 212. The greatest factor of 212 is 212.

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 212 and 217?

Answer:

Least Common Multiple of 212 and 217 = 46004

Step 1: Find the prime factorization of 212

212 = 2 x 2 x 53

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 = 46004 = 2 x 2 x 7 x 31 x 53

Step 4: Therefore, the least common multiple of 212 and 217 is 46004.