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 310 the smallest integer that is 9300 that is divisible by both numbers.
Least Common Multiple (LCM) of 300 and 310 is 9300.
LCM(300,310) = 9300
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 300 and 310. First we will calculate the prime factors of 300 and 310.
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 310
2 | 310 |
5 | 155 |
31 | 31 |
1 |
Prime factors of 310 are 2, 5,31. Prime factorization of 310 in exponential form is:
310 = 21×51×311
Now multiplying the highest exponent prime factors to calculate the LCM of 300 and 310.
LCM(300,310) = 22×31×52×311
LCM(300,310) = 9300
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 310
List of positive integer factors of 310 that divides 310 without a remainder.
1, 2, 5, 10, 31, 62, 155, 310
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 300 and 310, than apply into the LCM equation.
GCF(300,310) = 10
LCM(300,310) = ( 300 × 310) / 10
LCM(300,310) = 93000 / 10
LCM(300,310) = 9300
(i) The LCM of 310 and 300 is associative
LCM of 300 and 310 = LCM of 310 and 300
1. What is the LCM of 300 and 310?
Answer: LCM of 300 and 310 is 9300.
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 310?
Answer: Factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310. There are 8 integers that are factors of 310. The greatest factor of 310 is 310.
4. How to Find the LCM of 300 and 310?
Answer:
Least Common Multiple of 300 and 310 = 9300
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 310
310 = 2 x 5 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 = 9300 = 2 x 2 x 3 x 5 x 5 x 31
Step 4: Therefore, the least common multiple of 300 and 310 is 9300.