Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 902 and 909 the smallest integer that is 819918 that is divisible by both numbers.
Least Common Multiple (LCM) of 902 and 909 is 819918.
LCM(902,909) = 819918
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 902 and 909. First we will calculate the prime factors of 902 and 909.
Prime Factorization of 902
2 | 902 |
11 | 451 |
41 | 41 |
1 |
Prime factors of 902 are 2, 11,41. Prime factorization of 902 in exponential form is:
902 = 21×111×411
Prime Factorization of 909
3 | 909 |
3 | 303 |
101 | 101 |
1 |
Prime factors of 909 are 3,101. Prime factorization of 909 in exponential form is:
909 = 32×1011
Now multiplying the highest exponent prime factors to calculate the LCM of 902 and 909.
LCM(902,909) = 21×32×111×411×1011
LCM(902,909) = 819918
Factors of 902
List of positive integer factors of 902 that divides 902 without a remainder.
1, 2, 11, 22, 41, 82, 451, 902
Factors of 909
List of positive integer factors of 909 that divides 909 without a remainder.
1, 3, 9, 101, 303, 909
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 902 and 909, than apply into the LCM equation.
GCF(902,909) = 1
LCM(902,909) = ( 902 × 909) / 1
LCM(902,909) = 819918 / 1
LCM(902,909) = 819918
(i) The LCM of 909 and 902 is associative
LCM of 902 and 909 = LCM of 909 and 902
1. What is the LCM of 902 and 909?
Answer: LCM of 902 and 909 is 819918.
2. What are the Factors of 902?
Answer: Factors of 902 are 1, 2, 11, 22, 41, 82, 451, 902. There are 8 integers that are factors of 902. The greatest factor of 902 is 902.
3. What are the Factors of 909?
Answer: Factors of 909 are 1, 3, 9, 101, 303, 909. There are 6 integers that are factors of 909. The greatest factor of 909 is 909.
4. How to Find the LCM of 902 and 909?
Answer:
Least Common Multiple of 902 and 909 = 819918
Step 1: Find the prime factorization of 902
902 = 2 x 11 x 41
Step 2: Find the prime factorization of 909
909 = 3 x 3 x 101
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 819918 = 2 x 3 x 3 x 11 x 41 x 101
Step 4: Therefore, the least common multiple of 902 and 909 is 819918.