Least Common Multiple of 208 and 210

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 208 and 210 the smallest integer that is 21840 that is divisible by both numbers.

Least Common Multiple (LCM) of 208 and 210 is 21840.

LCM(208,210) = 21840

LCM of 208 and 210

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

LCM of:
and

Least Common Multiple of 208 and 210

LCM of 208 and 210 is 21840

Least common multiple can be found by multiplying the highest exponent prime factors of 208 and 210. First we will calculate the prime factors of 208 and 210.

Prime Factorization of 208


2 208
2 104
2 52
2 26
13 13
1

Prime factors of 208 are 2,13. Prime factorization of 208 in exponential form is:

208 = 24×131

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

Now multiplying the highest exponent prime factors to calculate the LCM of 208 and 210.

LCM(208,210) = 24×31×51×71×131
LCM(208,210) = 21840

Factors of 208

List of positive integer factors of 208 that divides 208 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 208

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

Least Common Multiple of 208 and 210 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 208 and 210, than apply into the LCM equation.

GCF(208,210) = 2
LCM(208,210) = ( 208 × 210) / 2
LCM(208,210) = 43680 / 2
LCM(208,210) = 21840

Properties of LCM 208 and 210

(i) The LCM of 210 and 208 is associative

LCM of 208 and 210 = LCM of 210 and 208

Related Least Common Multiples of 208

Related Least Common Multiples of 210

Frequently Asked Questions on LCM of 208 and 210

1. What is the LCM of 208 and 210?

Answer: LCM of 208 and 210 is 21840.

2. What are the Factors of 208?

Answer: Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. There are 10 integers that are factors of 208. The greatest factor of 208 is 208.

3. 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.

4. How to Find the LCM of 208 and 210?

Answer:

Least Common Multiple of 208 and 210 = 21840

Step 1: Find the prime factorization of 208

208 = 2 x 2 x 2 x 2 x 13

Step 2: Find the prime factorization of 210

210 = 2 x 3 x 5 x 7

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

LCM = 21840 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 208 and 210 is 21840.