Least Common Multiple of 214 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 214 and 219 the smallest integer that is 46866 that is divisible by both numbers.

Least Common Multiple (LCM) of 214 and 219 is 46866.

LCM(214,219) = 46866

LCM of 214 and 219

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

LCM of:
and

Least Common Multiple of 214 and 219

LCM of 214 and 219 is 46866

Least common multiple can be found by multiplying the highest exponent prime factors of 214 and 219. First we will calculate the prime factors of 214 and 219.

Prime Factorization of 214


2 214
107 107
1

Prime factors of 214 are 2,107. Prime factorization of 214 in exponential form is:

214 = 21×1071

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 214 and 219.

LCM(214,219) = 21×31×731×1071
LCM(214,219) = 46866

Factors of 214

List of positive integer factors of 214 that divides 214 without a remainder.

1, 2, 107, 214

Factors of 219

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

1, 3, 73, 219

Least Common Multiple of 214 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 214 and 219, than apply into the LCM equation.

GCF(214,219) = 1
LCM(214,219) = ( 214 × 219) / 1
LCM(214,219) = 46866 / 1
LCM(214,219) = 46866

Properties of LCM 214 and 219

(i) The LCM of 219 and 214 is associative

LCM of 214 and 219 = LCM of 219 and 214

Related Least Common Multiples of 214

Related Least Common Multiples of 219

Frequently Asked Questions on LCM of 214 and 219

1. What is the LCM of 214 and 219?

Answer: LCM of 214 and 219 is 46866.

2. What are the Factors of 214?

Answer: Factors of 214 are 1, 2, 107, 214. There are 4 integers that are factors of 214. The greatest factor of 214 is 214.

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 214 and 219?

Answer:

Least Common Multiple of 214 and 219 = 46866

Step 1: Find the prime factorization of 214

214 = 2 x 107

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 = 46866 = 2 x 3 x 73 x 107

Step 4: Therefore, the least common multiple of 214 and 219 is 46866.