Least Common Multiple of 212 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 212 and 219 the smallest integer that is 46428 that is divisible by both numbers.

Least Common Multiple (LCM) of 212 and 219 is 46428.

LCM(212,219) = 46428

LCM of 212 and 219

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

LCM of:
and

Least Common Multiple of 212 and 219

LCM of 212 and 219 is 46428

Least common multiple can be found by multiplying the highest exponent prime factors of 212 and 219. First we will calculate the prime factors of 212 and 219.

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 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 212 and 219.

LCM(212,219) = 22×31×531×731
LCM(212,219) = 46428

Factors of 212

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

1, 2, 4, 53, 106, 212

Factors of 219

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

1, 3, 73, 219

Least Common Multiple of 212 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 212 and 219, than apply into the LCM equation.

GCF(212,219) = 1
LCM(212,219) = ( 212 × 219) / 1
LCM(212,219) = 46428 / 1
LCM(212,219) = 46428

Properties of LCM 212 and 219

(i) The LCM of 219 and 212 is associative

LCM of 212 and 219 = LCM of 219 and 212

Related Least Common Multiples of 212

Related Least Common Multiples of 219

Frequently Asked Questions on LCM of 212 and 219

1. What is the LCM of 212 and 219?

Answer: LCM of 212 and 219 is 46428.

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 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 212 and 219?

Answer:

Least Common Multiple of 212 and 219 = 46428

Step 1: Find the prime factorization of 212

212 = 2 x 2 x 53

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 = 46428 = 2 x 2 x 3 x 53 x 73

Step 4: Therefore, the least common multiple of 212 and 219 is 46428.