Least Common Multiple of 212 and 213

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 213 the smallest integer that is 45156 that is divisible by both numbers.

Least Common Multiple (LCM) of 212 and 213 is 45156.

LCM(212,213) = 45156

LCM of 212 and 213

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

LCM of:
and

Least Common Multiple of 212 and 213

LCM of 212 and 213 is 45156

Least common multiple can be found by multiplying the highest exponent prime factors of 212 and 213. First we will calculate the prime factors of 212 and 213.

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 213


3 213
71 71
1

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

213 = 31×711

Now multiplying the highest exponent prime factors to calculate the LCM of 212 and 213.

LCM(212,213) = 22×31×531×711
LCM(212,213) = 45156

Factors of 212

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

1, 2, 4, 53, 106, 212

Factors of 213

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

1, 3, 71, 213

Least Common Multiple of 212 and 213 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 213, than apply into the LCM equation.

GCF(212,213) = 1
LCM(212,213) = ( 212 × 213) / 1
LCM(212,213) = 45156 / 1
LCM(212,213) = 45156

Properties of LCM 212 and 213

(i) The LCM of 213 and 212 is associative

LCM of 212 and 213 = LCM of 213 and 212

Related Least Common Multiples of 212

Related Least Common Multiples of 213

Frequently Asked Questions on LCM of 212 and 213

1. What is the LCM of 212 and 213?

Answer: LCM of 212 and 213 is 45156.

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 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.

4. How to Find the LCM of 212 and 213?

Answer:

Least Common Multiple of 212 and 213 = 45156

Step 1: Find the prime factorization of 212

212 = 2 x 2 x 53

Step 2: Find the prime factorization of 213

213 = 3 x 71

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

LCM = 45156 = 2 x 2 x 3 x 53 x 71

Step 4: Therefore, the least common multiple of 212 and 213 is 45156.