Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8216 and 8220 the smallest integer that is 16883880 that is divisible by both numbers.
Least Common Multiple (LCM) of 8216 and 8220 is 16883880.
LCM(8216,8220) = 16883880
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 8216 and 8220. First we will calculate the prime factors of 8216 and 8220.
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
Prime Factorization of 8220
2 | 8220 |
2 | 4110 |
3 | 2055 |
5 | 685 |
137 | 137 |
1 |
Prime factors of 8220 are 2, 3, 5,137. Prime factorization of 8220 in exponential form is:
8220 = 22×31×51×1371
Now multiplying the highest exponent prime factors to calculate the LCM of 8216 and 8220.
LCM(8216,8220) = 23×31×51×131×791×1371
LCM(8216,8220) = 16883880
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
Factors of 8220
List of positive integer factors of 8220 that divides 8220 without a remainder.
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 137, 274, 411, 548, 685, 822, 1370, 1644, 2055, 2740, 4110, 8220
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8216 and 8220, than apply into the LCM equation.
GCF(8216,8220) = 4
LCM(8216,8220) = ( 8216 × 8220) / 4
LCM(8216,8220) = 67535520 / 4
LCM(8216,8220) = 16883880
(i) The LCM of 8220 and 8216 is associative
LCM of 8216 and 8220 = LCM of 8220 and 8216
1. What is the LCM of 8216 and 8220?
Answer: LCM of 8216 and 8220 is 16883880.
2. 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.
3. What are the Factors of 8220?
Answer: Factors of 8220 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 137, 274, 411, 548, 685, 822, 1370, 1644, 2055, 2740, 4110, 8220. There are 24 integers that are factors of 8220. The greatest factor of 8220 is 8220.
4. How to Find the LCM of 8216 and 8220?
Answer:
Least Common Multiple of 8216 and 8220 = 16883880
Step 1: Find the prime factorization of 8216
8216 = 2 x 2 x 2 x 13 x 79
Step 2: Find the prime factorization of 8220
8220 = 2 x 2 x 3 x 5 x 137
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 16883880 = 2 x 2 x 2 x 3 x 5 x 13 x 79 x 137
Step 4: Therefore, the least common multiple of 8216 and 8220 is 16883880.