Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8218 and 8224 the smallest integer that is 33792416 that is divisible by both numbers.
Least Common Multiple (LCM) of 8218 and 8224 is 33792416.
LCM(8218,8224) = 33792416
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 8218 and 8224. First we will calculate the prime factors of 8218 and 8224.
Prime Factorization of 8218
2 | 8218 |
7 | 4109 |
587 | 587 |
1 |
Prime factors of 8218 are 2, 7,587. Prime factorization of 8218 in exponential form is:
8218 = 21×71×5871
Prime Factorization of 8224
2 | 8224 |
2 | 4112 |
2 | 2056 |
2 | 1028 |
2 | 514 |
257 | 257 |
1 |
Prime factors of 8224 are 2,257. Prime factorization of 8224 in exponential form is:
8224 = 25×2571
Now multiplying the highest exponent prime factors to calculate the LCM of 8218 and 8224.
LCM(8218,8224) = 25×71×2571×5871
LCM(8218,8224) = 33792416
Factors of 8218
List of positive integer factors of 8218 that divides 8218 without a remainder.
1, 2, 7, 14, 587, 1174, 4109, 8218
Factors of 8224
List of positive integer factors of 8224 that divides 8224 without a remainder.
1, 2, 4, 8, 16, 32, 257, 514, 1028, 2056, 4112, 8224
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8218 and 8224, than apply into the LCM equation.
GCF(8218,8224) = 2
LCM(8218,8224) = ( 8218 × 8224) / 2
LCM(8218,8224) = 67584832 / 2
LCM(8218,8224) = 33792416
(i) The LCM of 8224 and 8218 is associative
LCM of 8218 and 8224 = LCM of 8224 and 8218
1. What is the LCM of 8218 and 8224?
Answer: LCM of 8218 and 8224 is 33792416.
2. What are the Factors of 8218?
Answer: Factors of 8218 are 1, 2, 7, 14, 587, 1174, 4109, 8218. There are 8 integers that are factors of 8218. The greatest factor of 8218 is 8218.
3. What are the Factors of 8224?
Answer: Factors of 8224 are 1, 2, 4, 8, 16, 32, 257, 514, 1028, 2056, 4112, 8224. There are 12 integers that are factors of 8224. The greatest factor of 8224 is 8224.
4. How to Find the LCM of 8218 and 8224?
Answer:
Least Common Multiple of 8218 and 8224 = 33792416
Step 1: Find the prime factorization of 8218
8218 = 2 x 7 x 587
Step 2: Find the prime factorization of 8224
8224 = 2 x 2 x 2 x 2 x 2 x 257
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 33792416 = 2 x 2 x 2 x 2 x 2 x 7 x 257 x 587
Step 4: Therefore, the least common multiple of 8218 and 8224 is 33792416.