Least Common Multiple of 8214 and 8216

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 8214 and 8216 the smallest integer that is 33743112 that is divisible by both numbers.

Least Common Multiple (LCM) of 8214 and 8216 is 33743112.

LCM(8214,8216) = 33743112

LCM of 8214 and 8216

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

LCM of:
and

Least Common Multiple of 8214 and 8216

LCM of 8214 and 8216 is 33743112

Least common multiple can be found by multiplying the highest exponent prime factors of 8214 and 8216. First we will calculate the prime factors of 8214 and 8216.

Prime Factorization of 8214


2 8214
3 4107
37 1369
37 37
1

Prime factors of 8214 are 2, 3,37. Prime factorization of 8214 in exponential form is:

8214 = 21×31×372

Prime Factorization of 8216


2 8216
2 4108
2 2054
13 1027
79 79
1

Prime factors of 8216 are 2, 13,79. Prime factorization of 8216 in exponential form is:

8216 = 23×131×791

Now multiplying the highest exponent prime factors to calculate the LCM of 8214 and 8216.

LCM(8214,8216) = 23×31×131×372×791
LCM(8214,8216) = 33743112

Factors of 8214

List of positive integer factors of 8214 that divides 8214 without a remainder.

1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214

Factors of 8216

List of positive integer factors of 8216 that divides 8216 without a remainder.

1, 2, 4, 8, 13, 26, 52, 79, 104, 158, 316, 632, 1027, 2054, 4108, 8216

Least Common Multiple of 8214 and 8216 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8214 and 8216, than apply into the LCM equation.

GCF(8214,8216) = 2
LCM(8214,8216) = ( 8214 × 8216) / 2
LCM(8214,8216) = 67486224 / 2
LCM(8214,8216) = 33743112

Properties of LCM 8214 and 8216

(i) The LCM of 8216 and 8214 is associative

LCM of 8214 and 8216 = LCM of 8216 and 8214

Related Least Common Multiples of 8214

Related Least Common Multiples of 8216

Frequently Asked Questions on LCM of 8214 and 8216

1. What is the LCM of 8214 and 8216?

Answer: LCM of 8214 and 8216 is 33743112.

2. What are the Factors of 8214?

Answer: Factors of 8214 are 1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214. There are 12 integers that are factors of 8214. The greatest factor of 8214 is 8214.

3. What are the Factors of 8216?

Answer: Factors of 8216 are 1, 2, 4, 8, 13, 26, 52, 79, 104, 158, 316, 632, 1027, 2054, 4108, 8216. There are 16 integers that are factors of 8216. The greatest factor of 8216 is 8216.

4. How to Find the LCM of 8214 and 8216?

Answer:

Least Common Multiple of 8214 and 8216 = 33743112

Step 1: Find the prime factorization of 8214

8214 = 2 x 3 x 37 x 37

Step 2: Find the prime factorization of 8216

8216 = 2 x 2 x 2 x 13 x 79

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

LCM = 33743112 = 2 x 2 x 2 x 3 x 13 x 37 x 37 x 79

Step 4: Therefore, the least common multiple of 8214 and 8216 is 33743112.