Least Common Multiple of 210 and 214

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 210 and 214 the smallest integer that is 22470 that is divisible by both numbers.

Least Common Multiple (LCM) of 210 and 214 is 22470.

LCM(210,214) = 22470

LCM of 210 and 214

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

LCM of:
and

Least Common Multiple of 210 and 214

LCM of 210 and 214 is 22470

Least common multiple can be found by multiplying the highest exponent prime factors of 210 and 214. First we will calculate the prime factors of 210 and 214.

Prime Factorization of 210


2 210
3 105
5 35
7 7
1

Prime factors of 210 are 2, 3, 5,7. Prime factorization of 210 in exponential form is:

210 = 21×31×51×71

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

Now multiplying the highest exponent prime factors to calculate the LCM of 210 and 214.

LCM(210,214) = 21×31×51×71×1071
LCM(210,214) = 22470

Factors of 210

List of positive integer factors of 210 that divides 210 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

Factors of 214

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

1, 2, 107, 214

Least Common Multiple of 210 and 214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 210 and 214, than apply into the LCM equation.

GCF(210,214) = 2
LCM(210,214) = ( 210 × 214) / 2
LCM(210,214) = 44940 / 2
LCM(210,214) = 22470

Properties of LCM 210 and 214

(i) The LCM of 214 and 210 is associative

LCM of 210 and 214 = LCM of 214 and 210

Related Least Common Multiples of 210

Related Least Common Multiples of 214

Frequently Asked Questions on LCM of 210 and 214

1. What is the LCM of 210 and 214?

Answer: LCM of 210 and 214 is 22470.

2. What are the Factors of 210?

Answer: Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210. There are 16 integers that are factors of 210. The greatest factor of 210 is 210.

3. 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.

4. How to Find the LCM of 210 and 214?

Answer:

Least Common Multiple of 210 and 214 = 22470

Step 1: Find the prime factorization of 210

210 = 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 214

214 = 2 x 107

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

LCM = 22470 = 2 x 3 x 5 x 7 x 107

Step 4: Therefore, the least common multiple of 210 and 214 is 22470.