Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7424 and 7430 the smallest integer that is 27580160 that is divisible by both numbers.
Least Common Multiple (LCM) of 7424 and 7430 is 27580160.
LCM(7424,7430) = 27580160
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 7424 and 7430. First we will calculate the prime factors of 7424 and 7430.
Prime Factorization of 7424
2 | 7424 |
2 | 3712 |
2 | 1856 |
2 | 928 |
2 | 464 |
2 | 232 |
2 | 116 |
2 | 58 |
29 | 29 |
1 |
Prime factors of 7424 are 2,29. Prime factorization of 7424 in exponential form is:
7424 = 28×291
Prime Factorization of 7430
2 | 7430 |
5 | 3715 |
743 | 743 |
1 |
Prime factors of 7430 are 2, 5,743. Prime factorization of 7430 in exponential form is:
7430 = 21×51×7431
Now multiplying the highest exponent prime factors to calculate the LCM of 7424 and 7430.
LCM(7424,7430) = 28×51×291×7431
LCM(7424,7430) = 27580160
Factors of 7424
List of positive integer factors of 7424 that divides 7424 without a remainder.
1, 2, 4, 8, 16, 29, 32, 58, 64, 116, 128, 232, 256, 464, 928, 1856, 3712, 7424
Factors of 7430
List of positive integer factors of 7430 that divides 7430 without a remainder.
1, 2, 5, 10, 743, 1486, 3715, 7430
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7424 and 7430, than apply into the LCM equation.
GCF(7424,7430) = 2
LCM(7424,7430) = ( 7424 × 7430) / 2
LCM(7424,7430) = 55160320 / 2
LCM(7424,7430) = 27580160
(i) The LCM of 7430 and 7424 is associative
LCM of 7424 and 7430 = LCM of 7430 and 7424
1. What is the LCM of 7424 and 7430?
Answer: LCM of 7424 and 7430 is 27580160.
2. What are the Factors of 7424?
Answer: Factors of 7424 are 1, 2, 4, 8, 16, 29, 32, 58, 64, 116, 128, 232, 256, 464, 928, 1856, 3712, 7424. There are 18 integers that are factors of 7424. The greatest factor of 7424 is 7424.
3. What are the Factors of 7430?
Answer: Factors of 7430 are 1, 2, 5, 10, 743, 1486, 3715, 7430. There are 8 integers that are factors of 7430. The greatest factor of 7430 is 7430.
4. How to Find the LCM of 7424 and 7430?
Answer:
Least Common Multiple of 7424 and 7430 = 27580160
Step 1: Find the prime factorization of 7424
7424 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 29
Step 2: Find the prime factorization of 7430
7430 = 2 x 5 x 743
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 27580160 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 29 x 743
Step 4: Therefore, the least common multiple of 7424 and 7430 is 27580160.