Least Common Multiple of 214 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 214 and 216 the smallest integer that is 23112 that is divisible by both numbers.

Least Common Multiple (LCM) of 214 and 216 is 23112.

LCM(214,216) = 23112

LCM of 214 and 216

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

LCM of:
and

Least Common Multiple of 214 and 216

LCM of 214 and 216 is 23112

Least common multiple can be found by multiplying the highest exponent prime factors of 214 and 216. First we will calculate the prime factors of 214 and 216.

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 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 214 and 216.

LCM(214,216) = 23×33×1071
LCM(214,216) = 23112

Factors of 214

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

1, 2, 107, 214

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 214 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 214 and 216, than apply into the LCM equation.

GCF(214,216) = 2
LCM(214,216) = ( 214 × 216) / 2
LCM(214,216) = 46224 / 2
LCM(214,216) = 23112

Properties of LCM 214 and 216

(i) The LCM of 216 and 214 is associative

LCM of 214 and 216 = LCM of 216 and 214

Related Least Common Multiples of 214

Related Least Common Multiples of 216

Frequently Asked Questions on LCM of 214 and 216

1. What is the LCM of 214 and 216?

Answer: LCM of 214 and 216 is 23112.

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 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 214 and 216?

Answer:

Least Common Multiple of 214 and 216 = 23112

Step 1: Find the prime factorization of 214

214 = 2 x 107

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 = 23112 = 2 x 2 x 2 x 3 x 3 x 3 x 107

Step 4: Therefore, the least common multiple of 214 and 216 is 23112.