Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 4205 and 4210 the smallest integer that is 3540610 that is divisible by both numbers.
Least Common Multiple (LCM) of 4205 and 4210 is 3540610.
LCM(4205,4210) = 3540610
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 4205 and 4210. First we will calculate the prime factors of 4205 and 4210.
Prime Factorization of 4205
5 | 4205 |
29 | 841 |
29 | 29 |
1 |
Prime factors of 4205 are 5,29. Prime factorization of 4205 in exponential form is:
4205 = 51×292
Prime Factorization of 4210
2 | 4210 |
5 | 2105 |
421 | 421 |
1 |
Prime factors of 4210 are 2, 5,421. Prime factorization of 4210 in exponential form is:
4210 = 21×51×4211
Now multiplying the highest exponent prime factors to calculate the LCM of 4205 and 4210.
LCM(4205,4210) = 21×51×292×4211
LCM(4205,4210) = 3540610
Factors of 4205
List of positive integer factors of 4205 that divides 4205 without a remainder.
1, 5, 29, 145, 841, 4205
Factors of 4210
List of positive integer factors of 4210 that divides 4210 without a remainder.
1, 2, 5, 10, 421, 842, 2105, 4210
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4205 and 4210, than apply into the LCM equation.
GCF(4205,4210) = 5
LCM(4205,4210) = ( 4205 × 4210) / 5
LCM(4205,4210) = 17703050 / 5
LCM(4205,4210) = 3540610
(i) The LCM of 4210 and 4205 is associative
LCM of 4205 and 4210 = LCM of 4210 and 4205
1. What is the LCM of 4205 and 4210?
Answer: LCM of 4205 and 4210 is 3540610.
2. What are the Factors of 4205?
Answer: Factors of 4205 are 1, 5, 29, 145, 841, 4205. There are 6 integers that are factors of 4205. The greatest factor of 4205 is 4205.
3. What are the Factors of 4210?
Answer: Factors of 4210 are 1, 2, 5, 10, 421, 842, 2105, 4210. There are 8 integers that are factors of 4210. The greatest factor of 4210 is 4210.
4. How to Find the LCM of 4205 and 4210?
Answer:
Least Common Multiple of 4205 and 4210 = 3540610
Step 1: Find the prime factorization of 4205
4205 = 5 x 29 x 29
Step 2: Find the prime factorization of 4210
4210 = 2 x 5 x 421
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3540610 = 2 x 5 x 29 x 29 x 421
Step 4: Therefore, the least common multiple of 4205 and 4210 is 3540610.