Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 494 and 500 the smallest integer that is 123500 that is divisible by both numbers.
Least Common Multiple (LCM) of 494 and 500 is 123500.
LCM(494,500) = 123500
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 494 and 500. First we will calculate the prime factors of 494 and 500.
Prime Factorization of 494
2 | 494 |
13 | 247 |
19 | 19 |
1 |
Prime factors of 494 are 2, 13,19. Prime factorization of 494 in exponential form is:
494 = 21×131×191
Prime Factorization of 500
2 | 500 |
2 | 250 |
5 | 125 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 500 are 2,5. Prime factorization of 500 in exponential form is:
500 = 22×53
Now multiplying the highest exponent prime factors to calculate the LCM of 494 and 500.
LCM(494,500) = 22×53×131×191
LCM(494,500) = 123500
Factors of 494
List of positive integer factors of 494 that divides 494 without a remainder.
1, 2, 13, 19, 26, 38, 247, 494
Factors of 500
List of positive integer factors of 500 that divides 500 without a remainder.
1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 494 and 500, than apply into the LCM equation.
GCF(494,500) = 2
LCM(494,500) = ( 494 × 500) / 2
LCM(494,500) = 247000 / 2
LCM(494,500) = 123500
(i) The LCM of 500 and 494 is associative
LCM of 494 and 500 = LCM of 500 and 494
1. What is the LCM of 494 and 500?
Answer: LCM of 494 and 500 is 123500.
2. What are the Factors of 494?
Answer: Factors of 494 are 1, 2, 13, 19, 26, 38, 247, 494. There are 8 integers that are factors of 494. The greatest factor of 494 is 494.
3. What are the Factors of 500?
Answer: Factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500. There are 12 integers that are factors of 500. The greatest factor of 500 is 500.
4. How to Find the LCM of 494 and 500?
Answer:
Least Common Multiple of 494 and 500 = 123500
Step 1: Find the prime factorization of 494
494 = 2 x 13 x 19
Step 2: Find the prime factorization of 500
500 = 2 x 2 x 5 x 5 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 123500 = 2 x 2 x 5 x 5 x 5 x 13 x 19
Step 4: Therefore, the least common multiple of 494 and 500 is 123500.