Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2299 and 2305 the smallest integer that is 5299195 that is divisible by both numbers.
Least Common Multiple (LCM) of 2299 and 2305 is 5299195.
LCM(2299,2305) = 5299195
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 2299 and 2305. First we will calculate the prime factors of 2299 and 2305.
Prime Factorization of 2299
11 | 2299 |
11 | 209 |
19 | 19 |
1 |
Prime factors of 2299 are 11,19. Prime factorization of 2299 in exponential form is:
2299 = 112×191
Prime Factorization of 2305
5 | 2305 |
461 | 461 |
1 |
Prime factors of 2305 are 5,461. Prime factorization of 2305 in exponential form is:
2305 = 51×4611
Now multiplying the highest exponent prime factors to calculate the LCM of 2299 and 2305.
LCM(2299,2305) = 51×112×191×4611
LCM(2299,2305) = 5299195
Factors of 2299
List of positive integer factors of 2299 that divides 2299 without a remainder.
1, 11, 19, 121, 209, 2299
Factors of 2305
List of positive integer factors of 2305 that divides 2305 without a remainder.
1, 5, 461, 2305
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2299 and 2305, than apply into the LCM equation.
GCF(2299,2305) = 1
LCM(2299,2305) = ( 2299 × 2305) / 1
LCM(2299,2305) = 5299195 / 1
LCM(2299,2305) = 5299195
(i) The LCM of 2305 and 2299 is associative
LCM of 2299 and 2305 = LCM of 2305 and 2299
1. What is the LCM of 2299 and 2305?
Answer: LCM of 2299 and 2305 is 5299195.
2. What are the Factors of 2299?
Answer: Factors of 2299 are 1, 11, 19, 121, 209, 2299. There are 6 integers that are factors of 2299. The greatest factor of 2299 is 2299.
3. What are the Factors of 2305?
Answer: Factors of 2305 are 1, 5, 461, 2305. There are 4 integers that are factors of 2305. The greatest factor of 2305 is 2305.
4. How to Find the LCM of 2299 and 2305?
Answer:
Least Common Multiple of 2299 and 2305 = 5299195
Step 1: Find the prime factorization of 2299
2299 = 11 x 11 x 19
Step 2: Find the prime factorization of 2305
2305 = 5 x 461
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5299195 = 5 x 11 x 11 x 19 x 461
Step 4: Therefore, the least common multiple of 2299 and 2305 is 5299195.