Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2909 and 2912 the smallest integer that is 8471008 that is divisible by both numbers.
Least Common Multiple (LCM) of 2909 and 2912 is 8471008.
LCM(2909,2912) = 8471008
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 2909 and 2912. First we will calculate the prime factors of 2909 and 2912.
Prime Factorization of 2909
2909 | 2909 |
1 |
Prime factors of 2909 are 2909. Prime factorization of 2909 in exponential form is:
2909 = 29091
Prime Factorization of 2912
2 | 2912 |
2 | 1456 |
2 | 728 |
2 | 364 |
2 | 182 |
7 | 91 |
13 | 13 |
1 |
Prime factors of 2912 are 2, 7,13. Prime factorization of 2912 in exponential form is:
2912 = 25×71×131
Now multiplying the highest exponent prime factors to calculate the LCM of 2909 and 2912.
LCM(2909,2912) = 25×71×131×29091
LCM(2909,2912) = 8471008
Factors of 2909
List of positive integer factors of 2909 that divides 2909 without a remainder.
1, 2909
Factors of 2912
List of positive integer factors of 2912 that divides 2912 without a remainder.
1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 91, 104, 112, 182, 208, 224, 364, 416, 728, 1456, 2912
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2909 and 2912, than apply into the LCM equation.
GCF(2909,2912) = 1
LCM(2909,2912) = ( 2909 × 2912) / 1
LCM(2909,2912) = 8471008 / 1
LCM(2909,2912) = 8471008
(i) The LCM of 2912 and 2909 is associative
LCM of 2909 and 2912 = LCM of 2912 and 2909
1. What is the LCM of 2909 and 2912?
Answer: LCM of 2909 and 2912 is 8471008.
2. What are the Factors of 2909?
Answer: Factors of 2909 are 1, 2909. There are 2 integers that are factors of 2909. The greatest factor of 2909 is 2909.
3. What are the Factors of 2912?
Answer: Factors of 2912 are 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 91, 104, 112, 182, 208, 224, 364, 416, 728, 1456, 2912. There are 24 integers that are factors of 2912. The greatest factor of 2912 is 2912.
4. How to Find the LCM of 2909 and 2912?
Answer:
Least Common Multiple of 2909 and 2912 = 8471008
Step 1: Find the prime factorization of 2909
2909 = 2909
Step 2: Find the prime factorization of 2912
2912 = 2 x 2 x 2 x 2 x 2 x 7 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 8471008 = 2 x 2 x 2 x 2 x 2 x 7 x 13 x 2909
Step 4: Therefore, the least common multiple of 2909 and 2912 is 8471008.