Least Common Multiple of 210 and 216

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 216 the smallest integer that is 7560 that is divisible by both numbers.

Least Common Multiple (LCM) of 210 and 216 is 7560.

LCM(210,216) = 7560

LCM of 210 and 216

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

LCM of:
and

Least Common Multiple of 210 and 216

LCM of 210 and 216 is 7560

Least common multiple can be found by multiplying the highest exponent prime factors of 210 and 216. First we will calculate the prime factors of 210 and 216.

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 216


2 216
2 108
2 54
3 27
3 9
3 3
1

Prime factors of 216 are 2,3. Prime factorization of 216 in exponential form is:

216 = 23×33

Now multiplying the highest exponent prime factors to calculate the LCM of 210 and 216.

LCM(210,216) = 23×33×51×71
LCM(210,216) = 7560

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 216

List of positive integer factors of 216 that divides 216 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

Least Common Multiple of 210 and 216 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 216, than apply into the LCM equation.

GCF(210,216) = 6
LCM(210,216) = ( 210 × 216) / 6
LCM(210,216) = 45360 / 6
LCM(210,216) = 7560

Properties of LCM 210 and 216

(i) The LCM of 216 and 210 is associative

LCM of 210 and 216 = LCM of 216 and 210

Related Least Common Multiples of 210

Related Least Common Multiples of 216

Frequently Asked Questions on LCM of 210 and 216

1. What is the LCM of 210 and 216?

Answer: LCM of 210 and 216 is 7560.

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 216?

Answer: Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216. There are 16 integers that are factors of 216. The greatest factor of 216 is 216.

4. How to Find the LCM of 210 and 216?

Answer:

Least Common Multiple of 210 and 216 = 7560

Step 1: Find the prime factorization of 210

210 = 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 216

216 = 2 x 2 x 2 x 3 x 3 x 3

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

LCM = 7560 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 210 and 216 is 7560.