Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8217 and 8222 the smallest integer that is 67560174 that is divisible by both numbers.
Least Common Multiple (LCM) of 8217 and 8222 is 67560174.
LCM(8217,8222) = 67560174
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 8217 and 8222. First we will calculate the prime factors of 8217 and 8222.
Prime Factorization of 8217
3 | 8217 |
3 | 2739 |
11 | 913 |
83 | 83 |
1 |
Prime factors of 8217 are 3, 11,83. Prime factorization of 8217 in exponential form is:
8217 = 32×111×831
Prime Factorization of 8222
2 | 8222 |
4111 | 4111 |
1 |
Prime factors of 8222 are 2,4111. Prime factorization of 8222 in exponential form is:
8222 = 21×41111
Now multiplying the highest exponent prime factors to calculate the LCM of 8217 and 8222.
LCM(8217,8222) = 21×32×111×831×41111
LCM(8217,8222) = 67560174
Factors of 8217
List of positive integer factors of 8217 that divides 8217 without a remainder.
1, 3, 9, 11, 33, 83, 99, 249, 747, 913, 2739, 8217
Factors of 8222
List of positive integer factors of 8222 that divides 8222 without a remainder.
1, 2, 4111, 8222
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8217 and 8222, than apply into the LCM equation.
GCF(8217,8222) = 1
LCM(8217,8222) = ( 8217 × 8222) / 1
LCM(8217,8222) = 67560174 / 1
LCM(8217,8222) = 67560174
(i) The LCM of 8222 and 8217 is associative
LCM of 8217 and 8222 = LCM of 8222 and 8217
1. What is the LCM of 8217 and 8222?
Answer: LCM of 8217 and 8222 is 67560174.
2. What are the Factors of 8217?
Answer: Factors of 8217 are 1, 3, 9, 11, 33, 83, 99, 249, 747, 913, 2739, 8217. There are 12 integers that are factors of 8217. The greatest factor of 8217 is 8217.
3. What are the Factors of 8222?
Answer: Factors of 8222 are 1, 2, 4111, 8222. There are 4 integers that are factors of 8222. The greatest factor of 8222 is 8222.
4. How to Find the LCM of 8217 and 8222?
Answer:
Least Common Multiple of 8217 and 8222 = 67560174
Step 1: Find the prime factorization of 8217
8217 = 3 x 3 x 11 x 83
Step 2: Find the prime factorization of 8222
8222 = 2 x 4111
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 67560174 = 2 x 3 x 3 x 11 x 83 x 4111
Step 4: Therefore, the least common multiple of 8217 and 8222 is 67560174.