Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 17221 and 17224 the smallest integer that is 296614504 that is divisible by both numbers.
Least Common Multiple (LCM) of 17221 and 17224 is 296614504.
LCM(17221,17224) = 296614504
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 17221 and 17224. First we will calculate the prime factors of 17221 and 17224.
Prime Factorization of 17221
17 | 17221 |
1013 | 1013 |
1 |
Prime factors of 17221 are 17,1013. Prime factorization of 17221 in exponential form is:
17221 = 171×10131
Prime Factorization of 17224
2 | 17224 |
2 | 8612 |
2 | 4306 |
2153 | 2153 |
1 |
Prime factors of 17224 are 2,2153. Prime factorization of 17224 in exponential form is:
17224 = 23×21531
Now multiplying the highest exponent prime factors to calculate the LCM of 17221 and 17224.
LCM(17221,17224) = 23×171×10131×21531
LCM(17221,17224) = 296614504
Factors of 17221
List of positive integer factors of 17221 that divides 17221 without a remainder.
1, 17, 1013, 17221
Factors of 17224
List of positive integer factors of 17224 that divides 17224 without a remainder.
1, 2, 4, 8, 2153, 4306, 8612, 17224
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17221 and 17224, than apply into the LCM equation.
GCF(17221,17224) = 1
LCM(17221,17224) = ( 17221 × 17224) / 1
LCM(17221,17224) = 296614504 / 1
LCM(17221,17224) = 296614504
(i) The LCM of 17224 and 17221 is associative
LCM of 17221 and 17224 = LCM of 17224 and 17221
1. What is the LCM of 17221 and 17224?
Answer: LCM of 17221 and 17224 is 296614504.
2. What are the Factors of 17221?
Answer: Factors of 17221 are 1, 17, 1013, 17221. There are 4 integers that are factors of 17221. The greatest factor of 17221 is 17221.
3. What are the Factors of 17224?
Answer: Factors of 17224 are 1, 2, 4, 8, 2153, 4306, 8612, 17224. There are 8 integers that are factors of 17224. The greatest factor of 17224 is 17224.
4. How to Find the LCM of 17221 and 17224?
Answer:
Least Common Multiple of 17221 and 17224 = 296614504
Step 1: Find the prime factorization of 17221
17221 = 17 x 1013
Step 2: Find the prime factorization of 17224
17224 = 2 x 2 x 2 x 2153
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 296614504 = 2 x 2 x 2 x 17 x 1013 x 2153
Step 4: Therefore, the least common multiple of 17221 and 17224 is 296614504.