Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6300 and 6305 the smallest integer that is 7944300 that is divisible by both numbers.
Least Common Multiple (LCM) of 6300 and 6305 is 7944300.
LCM(6300,6305) = 7944300
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 6300 and 6305. First we will calculate the prime factors of 6300 and 6305.
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
Prime Factorization of 6305
5 | 6305 |
13 | 1261 |
97 | 97 |
1 |
Prime factors of 6305 are 5, 13,97. Prime factorization of 6305 in exponential form is:
6305 = 51×131×971
Now multiplying the highest exponent prime factors to calculate the LCM of 6300 and 6305.
LCM(6300,6305) = 22×32×52×71×131×971
LCM(6300,6305) = 7944300
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
Factors of 6305
List of positive integer factors of 6305 that divides 6305 without a remainder.
1, 5, 13, 65, 97, 485, 1261, 6305
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6300 and 6305, than apply into the LCM equation.
GCF(6300,6305) = 5
LCM(6300,6305) = ( 6300 × 6305) / 5
LCM(6300,6305) = 39721500 / 5
LCM(6300,6305) = 7944300
(i) The LCM of 6305 and 6300 is associative
LCM of 6300 and 6305 = LCM of 6305 and 6300
1. What is the LCM of 6300 and 6305?
Answer: LCM of 6300 and 6305 is 7944300.
2. 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.
3. What are the Factors of 6305?
Answer: Factors of 6305 are 1, 5, 13, 65, 97, 485, 1261, 6305. There are 8 integers that are factors of 6305. The greatest factor of 6305 is 6305.
4. How to Find the LCM of 6300 and 6305?
Answer:
Least Common Multiple of 6300 and 6305 = 7944300
Step 1: Find the prime factorization of 6300
6300 = 2 x 2 x 3 x 3 x 5 x 5 x 7
Step 2: Find the prime factorization of 6305
6305 = 5 x 13 x 97
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7944300 = 2 x 2 x 3 x 3 x 5 x 5 x 7 x 13 x 97
Step 4: Therefore, the least common multiple of 6300 and 6305 is 7944300.