Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 5296 and 5300 the smallest integer that is 7017200 that is divisible by both numbers.
Least Common Multiple (LCM) of 5296 and 5300 is 7017200.
LCM(5296,5300) = 7017200
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 5296 and 5300. First we will calculate the prime factors of 5296 and 5300.
Prime Factorization of 5296
2 | 5296 |
2 | 2648 |
2 | 1324 |
2 | 662 |
331 | 331 |
1 |
Prime factors of 5296 are 2,331. Prime factorization of 5296 in exponential form is:
5296 = 24×3311
Prime Factorization of 5300
2 | 5300 |
2 | 2650 |
5 | 1325 |
5 | 265 |
53 | 53 |
1 |
Prime factors of 5300 are 2, 5,53. Prime factorization of 5300 in exponential form is:
5300 = 22×52×531
Now multiplying the highest exponent prime factors to calculate the LCM of 5296 and 5300.
LCM(5296,5300) = 24×52×531×3311
LCM(5296,5300) = 7017200
Factors of 5296
List of positive integer factors of 5296 that divides 5296 without a remainder.
1, 2, 4, 8, 16, 331, 662, 1324, 2648, 5296
Factors of 5300
List of positive integer factors of 5300 that divides 5300 without a remainder.
1, 2, 4, 5, 10, 20, 25, 50, 53, 100, 106, 212, 265, 530, 1060, 1325, 2650, 5300
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5296 and 5300, than apply into the LCM equation.
GCF(5296,5300) = 4
LCM(5296,5300) = ( 5296 × 5300) / 4
LCM(5296,5300) = 28068800 / 4
LCM(5296,5300) = 7017200
(i) The LCM of 5300 and 5296 is associative
LCM of 5296 and 5300 = LCM of 5300 and 5296
1. What is the LCM of 5296 and 5300?
Answer: LCM of 5296 and 5300 is 7017200.
2. What are the Factors of 5296?
Answer: Factors of 5296 are 1, 2, 4, 8, 16, 331, 662, 1324, 2648, 5296. There are 10 integers that are factors of 5296. The greatest factor of 5296 is 5296.
3. What are the Factors of 5300?
Answer: Factors of 5300 are 1, 2, 4, 5, 10, 20, 25, 50, 53, 100, 106, 212, 265, 530, 1060, 1325, 2650, 5300. There are 18 integers that are factors of 5300. The greatest factor of 5300 is 5300.
4. How to Find the LCM of 5296 and 5300?
Answer:
Least Common Multiple of 5296 and 5300 = 7017200
Step 1: Find the prime factorization of 5296
5296 = 2 x 2 x 2 x 2 x 331
Step 2: Find the prime factorization of 5300
5300 = 2 x 2 x 5 x 5 x 53
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7017200 = 2 x 2 x 2 x 2 x 5 x 5 x 53 x 331
Step 4: Therefore, the least common multiple of 5296 and 5300 is 7017200.