Least Common Multiple of 300 and 305
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 300 and 305 the smallest integer that is 18300 that is divisible by both numbers.
Least Common Multiple (LCM) of 300 and 305 is 18300.
LCM(300,305) = 18300
LCM of 300 and 305
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 300 and 305 by Prime method
- Least Common Multiple of 300 and 305 with GCF Formula
LCM of 300 and 305 is 18300
Least common multiple can be found by multiplying the highest exponent prime factors of 300 and 305. First we will calculate the prime factors of 300 and 305.
Prime Factorization of 300
| 2 | 300 |
| 2 | 150 |
| 3 | 75 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 300 are 2, 3,5. Prime factorization of 300 in exponential form is:
300 = 22×31×52
Prime Factorization of 305
| 5 | 305 |
| 61 | 61 |
| 1 |
Prime factors of 305 are 5,61. Prime factorization of 305 in exponential form is:
305 = 51×611
Now multiplying the highest exponent prime factors to calculate the LCM of 300 and 305.
LCM(300,305) = 22×31×52×611
LCM(300,305) = 18300
Factors of 300
List of positive integer factors of 300 that divides 300 without a remainder.
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Factors of 305
List of positive integer factors of 305 that divides 305 without a remainder.
1, 5, 61, 305
Least Common Multiple of 300 and 305 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 300 and 305, than apply into the LCM equation.
GCF(300,305) = 5
LCM(300,305) = ( 300 × 305) / 5
LCM(300,305) = 91500 / 5
LCM(300,305) = 18300
Properties of LCM 300 and 305
(i) The LCM of 305 and 300 is associative
LCM of 300 and 305 = LCM of 305 and 300
Related Least Common Multiples of 300
Related Least Common Multiples of 305
Frequently Asked Questions on LCM of 300 and 305
1. What is the LCM of 300 and 305?
Answer: LCM of 300 and 305 is 18300.
2. What are the Factors of 300?
Answer: Factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300. There are 18 integers that are factors of 300. The greatest factor of 300 is 300.
3. What are the Factors of 305?
Answer: Factors of 305 are 1, 5, 61, 305. There are 4 integers that are factors of 305. The greatest factor of 305 is 305.
4. How to Find the LCM of 300 and 305?
Answer:
Least Common Multiple of 300 and 305 = 18300
Step 1: Find the prime factorization of 300
300 = 2 x 2 x 3 x 5 x 5
Step 2: Find the prime factorization of 305
305 = 5 x 61
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 18300 = 2 x 2 x 3 x 5 x 5 x 61
Step 4: Therefore, the least common multiple of 300 and 305 is 18300.
