Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6410 and 6417 the smallest integer that is 41132970 that is divisible by both numbers.
Least Common Multiple (LCM) of 6410 and 6417 is 41132970.
LCM(6410,6417) = 41132970
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 6410 and 6417. First we will calculate the prime factors of 6410 and 6417.
Prime Factorization of 6410
2 | 6410 |
5 | 3205 |
641 | 641 |
1 |
Prime factors of 6410 are 2, 5,641. Prime factorization of 6410 in exponential form is:
6410 = 21×51×6411
Prime Factorization of 6417
3 | 6417 |
3 | 2139 |
23 | 713 |
31 | 31 |
1 |
Prime factors of 6417 are 3, 23,31. Prime factorization of 6417 in exponential form is:
6417 = 32×231×311
Now multiplying the highest exponent prime factors to calculate the LCM of 6410 and 6417.
LCM(6410,6417) = 21×32×51×231×311×6411
LCM(6410,6417) = 41132970
Factors of 6410
List of positive integer factors of 6410 that divides 6410 without a remainder.
1, 2, 5, 10, 641, 1282, 3205, 6410
Factors of 6417
List of positive integer factors of 6417 that divides 6417 without a remainder.
1, 3, 9, 23, 31, 69, 93, 207, 279, 713, 2139, 6417
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6410 and 6417, than apply into the LCM equation.
GCF(6410,6417) = 1
LCM(6410,6417) = ( 6410 × 6417) / 1
LCM(6410,6417) = 41132970 / 1
LCM(6410,6417) = 41132970
(i) The LCM of 6417 and 6410 is associative
LCM of 6410 and 6417 = LCM of 6417 and 6410
1. What is the LCM of 6410 and 6417?
Answer: LCM of 6410 and 6417 is 41132970.
2. What are the Factors of 6410?
Answer: Factors of 6410 are 1, 2, 5, 10, 641, 1282, 3205, 6410. There are 8 integers that are factors of 6410. The greatest factor of 6410 is 6410.
3. What are the Factors of 6417?
Answer: Factors of 6417 are 1, 3, 9, 23, 31, 69, 93, 207, 279, 713, 2139, 6417. There are 12 integers that are factors of 6417. The greatest factor of 6417 is 6417.
4. How to Find the LCM of 6410 and 6417?
Answer:
Least Common Multiple of 6410 and 6417 = 41132970
Step 1: Find the prime factorization of 6410
6410 = 2 x 5 x 641
Step 2: Find the prime factorization of 6417
6417 = 3 x 3 x 23 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 41132970 = 2 x 3 x 3 x 5 x 23 x 31 x 641
Step 4: Therefore, the least common multiple of 6410 and 6417 is 41132970.