Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 990 and 998 the smallest integer that is 494010 that is divisible by both numbers.
Least Common Multiple (LCM) of 990 and 998 is 494010.
LCM(990,998) = 494010
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 990 and 998. First we will calculate the prime factors of 990 and 998.
Prime Factorization of 990
2 | 990 |
3 | 495 |
3 | 165 |
5 | 55 |
11 | 11 |
1 |
Prime factors of 990 are 2, 3, 5,11. Prime factorization of 990 in exponential form is:
990 = 21×32×51×111
Prime Factorization of 998
2 | 998 |
499 | 499 |
1 |
Prime factors of 998 are 2,499. Prime factorization of 998 in exponential form is:
998 = 21×4991
Now multiplying the highest exponent prime factors to calculate the LCM of 990 and 998.
LCM(990,998) = 21×32×51×111×4991
LCM(990,998) = 494010
Factors of 990
List of positive integer factors of 990 that divides 990 without a remainder.
1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990
Factors of 998
List of positive integer factors of 998 that divides 998 without a remainder.
1, 2, 499, 998
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 990 and 998, than apply into the LCM equation.
GCF(990,998) = 2
LCM(990,998) = ( 990 × 998) / 2
LCM(990,998) = 988020 / 2
LCM(990,998) = 494010
(i) The LCM of 998 and 990 is associative
LCM of 990 and 998 = LCM of 998 and 990
1. What is the LCM of 990 and 998?
Answer: LCM of 990 and 998 is 494010.
2. What are the Factors of 990?
Answer: Factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990. There are 24 integers that are factors of 990. The greatest factor of 990 is 990.
3. What are the Factors of 998?
Answer: Factors of 998 are 1, 2, 499, 998. There are 4 integers that are factors of 998. The greatest factor of 998 is 998.
4. How to Find the LCM of 990 and 998?
Answer:
Least Common Multiple of 990 and 998 = 494010
Step 1: Find the prime factorization of 990
990 = 2 x 3 x 3 x 5 x 11
Step 2: Find the prime factorization of 998
998 = 2 x 499
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 494010 = 2 x 3 x 3 x 5 x 11 x 499
Step 4: Therefore, the least common multiple of 990 and 998 is 494010.