Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 5314 and 5321 the smallest integer that is 28275794 that is divisible by both numbers.
Least Common Multiple (LCM) of 5314 and 5321 is 28275794.
LCM(5314,5321) = 28275794
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 5314 and 5321. First we will calculate the prime factors of 5314 and 5321.
Prime Factorization of 5314
2 | 5314 |
2657 | 2657 |
1 |
Prime factors of 5314 are 2,2657. Prime factorization of 5314 in exponential form is:
5314 = 21×26571
Prime Factorization of 5321
17 | 5321 |
313 | 313 |
1 |
Prime factors of 5321 are 17,313. Prime factorization of 5321 in exponential form is:
5321 = 171×3131
Now multiplying the highest exponent prime factors to calculate the LCM of 5314 and 5321.
LCM(5314,5321) = 21×171×3131×26571
LCM(5314,5321) = 28275794
Factors of 5314
List of positive integer factors of 5314 that divides 5314 without a remainder.
1, 2, 2657, 5314
Factors of 5321
List of positive integer factors of 5321 that divides 5321 without a remainder.
1, 17, 313, 5321
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5314 and 5321, than apply into the LCM equation.
GCF(5314,5321) = 1
LCM(5314,5321) = ( 5314 × 5321) / 1
LCM(5314,5321) = 28275794 / 1
LCM(5314,5321) = 28275794
(i) The LCM of 5321 and 5314 is associative
LCM of 5314 and 5321 = LCM of 5321 and 5314
1. What is the LCM of 5314 and 5321?
Answer: LCM of 5314 and 5321 is 28275794.
2. What are the Factors of 5314?
Answer: Factors of 5314 are 1, 2, 2657, 5314. There are 4 integers that are factors of 5314. The greatest factor of 5314 is 5314.
3. What are the Factors of 5321?
Answer: Factors of 5321 are 1, 17, 313, 5321. There are 4 integers that are factors of 5321. The greatest factor of 5321 is 5321.
4. How to Find the LCM of 5314 and 5321?
Answer:
Least Common Multiple of 5314 and 5321 = 28275794
Step 1: Find the prime factorization of 5314
5314 = 2 x 2657
Step 2: Find the prime factorization of 5321
5321 = 17 x 313
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 28275794 = 2 x 17 x 313 x 2657
Step 4: Therefore, the least common multiple of 5314 and 5321 is 28275794.