Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6293 and 6300 the smallest integer that is 5663700 that is divisible by both numbers.
Least Common Multiple (LCM) of 6293 and 6300 is 5663700.
LCM(6293,6300) = 5663700
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 6293 and 6300. First we will calculate the prime factors of 6293 and 6300.
Prime Factorization of 6293
7 | 6293 |
29 | 899 |
31 | 31 |
1 |
Prime factors of 6293 are 7, 29,31. Prime factorization of 6293 in exponential form is:
6293 = 71×291×311
Prime Factorization of 6300
2 | 6300 |
2 | 3150 |
3 | 1575 |
3 | 525 |
5 | 175 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 6300 are 2, 3, 5,7. Prime factorization of 6300 in exponential form is:
6300 = 22×32×52×71
Now multiplying the highest exponent prime factors to calculate the LCM of 6293 and 6300.
LCM(6293,6300) = 22×32×52×71×291×311
LCM(6293,6300) = 5663700
Factors of 6293
List of positive integer factors of 6293 that divides 6293 without a remainder.
1, 7, 29, 31, 203, 217, 899, 6293
Factors of 6300
List of positive integer factors of 6300 that divides 6300 without a remainder.
1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 126, 140, 150, 175, 180, 210, 225, 252, 300, 315, 350, 420, 450, 525, 630, 700, 900, 1050, 1260, 1575, 2100, 3150, 6300
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6293 and 6300, than apply into the LCM equation.
GCF(6293,6300) = 7
LCM(6293,6300) = ( 6293 × 6300) / 7
LCM(6293,6300) = 39645900 / 7
LCM(6293,6300) = 5663700
(i) The LCM of 6300 and 6293 is associative
LCM of 6293 and 6300 = LCM of 6300 and 6293
1. What is the LCM of 6293 and 6300?
Answer: LCM of 6293 and 6300 is 5663700.
2. What are the Factors of 6293?
Answer: Factors of 6293 are 1, 7, 29, 31, 203, 217, 899, 6293. There are 8 integers that are factors of 6293. The greatest factor of 6293 is 6293.
3. What are the Factors of 6300?
Answer: Factors of 6300 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 126, 140, 150, 175, 180, 210, 225, 252, 300, 315, 350, 420, 450, 525, 630, 700, 900, 1050, 1260, 1575, 2100, 3150, 6300. There are 54 integers that are factors of 6300. The greatest factor of 6300 is 6300.
4. How to Find the LCM of 6293 and 6300?
Answer:
Least Common Multiple of 6293 and 6300 = 5663700
Step 1: Find the prime factorization of 6293
6293 = 7 x 29 x 31
Step 2: Find the prime factorization of 6300
6300 = 2 x 2 x 3 x 3 x 5 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5663700 = 2 x 2 x 3 x 3 x 5 x 5 x 7 x 29 x 31
Step 4: Therefore, the least common multiple of 6293 and 6300 is 5663700.