Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8210 and 8212 the smallest integer that is 33710260 that is divisible by both numbers.
Least Common Multiple (LCM) of 8210 and 8212 is 33710260.
LCM(8210,8212) = 33710260
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 8210 and 8212. First we will calculate the prime factors of 8210 and 8212.
Prime Factorization of 8210
2 | 8210 |
5 | 4105 |
821 | 821 |
1 |
Prime factors of 8210 are 2, 5,821. Prime factorization of 8210 in exponential form is:
8210 = 21×51×8211
Prime Factorization of 8212
2 | 8212 |
2 | 4106 |
2053 | 2053 |
1 |
Prime factors of 8212 are 2,2053. Prime factorization of 8212 in exponential form is:
8212 = 22×20531
Now multiplying the highest exponent prime factors to calculate the LCM of 8210 and 8212.
LCM(8210,8212) = 22×51×8211×20531
LCM(8210,8212) = 33710260
Factors of 8210
List of positive integer factors of 8210 that divides 8210 without a remainder.
1, 2, 5, 10, 821, 1642, 4105, 8210
Factors of 8212
List of positive integer factors of 8212 that divides 8212 without a remainder.
1, 2, 4, 2053, 4106, 8212
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8210 and 8212, than apply into the LCM equation.
GCF(8210,8212) = 2
LCM(8210,8212) = ( 8210 × 8212) / 2
LCM(8210,8212) = 67420520 / 2
LCM(8210,8212) = 33710260
(i) The LCM of 8212 and 8210 is associative
LCM of 8210 and 8212 = LCM of 8212 and 8210
1. What is the LCM of 8210 and 8212?
Answer: LCM of 8210 and 8212 is 33710260.
2. What are the Factors of 8210?
Answer: Factors of 8210 are 1, 2, 5, 10, 821, 1642, 4105, 8210. There are 8 integers that are factors of 8210. The greatest factor of 8210 is 8210.
3. What are the Factors of 8212?
Answer: Factors of 8212 are 1, 2, 4, 2053, 4106, 8212. There are 6 integers that are factors of 8212. The greatest factor of 8212 is 8212.
4. How to Find the LCM of 8210 and 8212?
Answer:
Least Common Multiple of 8210 and 8212 = 33710260
Step 1: Find the prime factorization of 8210
8210 = 2 x 5 x 821
Step 2: Find the prime factorization of 8212
8212 = 2 x 2 x 2053
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 33710260 = 2 x 2 x 5 x 821 x 2053
Step 4: Therefore, the least common multiple of 8210 and 8212 is 33710260.