Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8219 and 8224 the smallest integer that is 67593056 that is divisible by both numbers.
Least Common Multiple (LCM) of 8219 and 8224 is 67593056.
LCM(8219,8224) = 67593056
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 8219 and 8224. First we will calculate the prime factors of 8219 and 8224.
Prime Factorization of 8219
8219 | 8219 |
1 |
Prime factors of 8219 are 8219. Prime factorization of 8219 in exponential form is:
8219 = 82191
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 8219 and 8224.
LCM(8219,8224) = 25×2571×82191
LCM(8219,8224) = 67593056
Factors of 8219
List of positive integer factors of 8219 that divides 8219 without a remainder.
1, 8219
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 8219 and 8224, than apply into the LCM equation.
GCF(8219,8224) = 1
LCM(8219,8224) = ( 8219 × 8224) / 1
LCM(8219,8224) = 67593056 / 1
LCM(8219,8224) = 67593056
(i) The LCM of 8224 and 8219 is associative
LCM of 8219 and 8224 = LCM of 8224 and 8219
1. What is the LCM of 8219 and 8224?
Answer: LCM of 8219 and 8224 is 67593056.
2. What are the Factors of 8219?
Answer: Factors of 8219 are 1, 8219. There are 2 integers that are factors of 8219. The greatest factor of 8219 is 8219.
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 8219 and 8224?
Answer:
Least Common Multiple of 8219 and 8224 = 67593056
Step 1: Find the prime factorization of 8219
8219 = 8219
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 = 67593056 = 2 x 2 x 2 x 2 x 2 x 257 x 8219
Step 4: Therefore, the least common multiple of 8219 and 8224 is 67593056.