Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 490 and 491 the smallest integer that is 240590 that is divisible by both numbers.
Least Common Multiple (LCM) of 490 and 491 is 240590.
LCM(490,491) = 240590
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 490 and 491. First we will calculate the prime factors of 490 and 491.
Prime Factorization of 490
2 | 490 |
5 | 245 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 490 are 2, 5,7. Prime factorization of 490 in exponential form is:
490 = 21×51×72
Prime Factorization of 491
491 | 491 |
1 |
Prime factors of 491 are 491. Prime factorization of 491 in exponential form is:
491 = 4911
Now multiplying the highest exponent prime factors to calculate the LCM of 490 and 491.
LCM(490,491) = 21×51×72×4911
LCM(490,491) = 240590
Factors of 490
List of positive integer factors of 490 that divides 490 without a remainder.
1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490
Factors of 491
List of positive integer factors of 491 that divides 491 without a remainder.
1, 491
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 490 and 491, than apply into the LCM equation.
GCF(490,491) = 1
LCM(490,491) = ( 490 × 491) / 1
LCM(490,491) = 240590 / 1
LCM(490,491) = 240590
(i) The LCM of 491 and 490 is associative
LCM of 490 and 491 = LCM of 491 and 490
1. What is the LCM of 490 and 491?
Answer: LCM of 490 and 491 is 240590.
2. What are the Factors of 490?
Answer: Factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490. There are 12 integers that are factors of 490. The greatest factor of 490 is 490.
3. What are the Factors of 491?
Answer: Factors of 491 are 1, 491. There are 2 integers that are factors of 491. The greatest factor of 491 is 491.
4. How to Find the LCM of 490 and 491?
Answer:
Least Common Multiple of 490 and 491 = 240590
Step 1: Find the prime factorization of 490
490 = 2 x 5 x 7 x 7
Step 2: Find the prime factorization of 491
491 = 491
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 240590 = 2 x 5 x 7 x 7 x 491
Step 4: Therefore, the least common multiple of 490 and 491 is 240590.