Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 5721 and 5728 the smallest integer that is 32769888 that is divisible by both numbers.
Least Common Multiple (LCM) of 5721 and 5728 is 32769888.
LCM(5721,5728) = 32769888
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 5721 and 5728. First we will calculate the prime factors of 5721 and 5728.
Prime Factorization of 5721
3 | 5721 |
1907 | 1907 |
1 |
Prime factors of 5721 are 3,1907. Prime factorization of 5721 in exponential form is:
5721 = 31×19071
Prime Factorization of 5728
2 | 5728 |
2 | 2864 |
2 | 1432 |
2 | 716 |
2 | 358 |
179 | 179 |
1 |
Prime factors of 5728 are 2,179. Prime factorization of 5728 in exponential form is:
5728 = 25×1791
Now multiplying the highest exponent prime factors to calculate the LCM of 5721 and 5728.
LCM(5721,5728) = 25×31×1791×19071
LCM(5721,5728) = 32769888
Factors of 5721
List of positive integer factors of 5721 that divides 5721 without a remainder.
1, 3, 1907, 5721
Factors of 5728
List of positive integer factors of 5728 that divides 5728 without a remainder.
1, 2, 4, 8, 16, 32, 179, 358, 716, 1432, 2864, 5728
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5721 and 5728, than apply into the LCM equation.
GCF(5721,5728) = 1
LCM(5721,5728) = ( 5721 × 5728) / 1
LCM(5721,5728) = 32769888 / 1
LCM(5721,5728) = 32769888
(i) The LCM of 5728 and 5721 is associative
LCM of 5721 and 5728 = LCM of 5728 and 5721
1. What is the LCM of 5721 and 5728?
Answer: LCM of 5721 and 5728 is 32769888.
2. What are the Factors of 5721?
Answer: Factors of 5721 are 1, 3, 1907, 5721. There are 4 integers that are factors of 5721. The greatest factor of 5721 is 5721.
3. What are the Factors of 5728?
Answer: Factors of 5728 are 1, 2, 4, 8, 16, 32, 179, 358, 716, 1432, 2864, 5728. There are 12 integers that are factors of 5728. The greatest factor of 5728 is 5728.
4. How to Find the LCM of 5721 and 5728?
Answer:
Least Common Multiple of 5721 and 5728 = 32769888
Step 1: Find the prime factorization of 5721
5721 = 3 x 1907
Step 2: Find the prime factorization of 5728
5728 = 2 x 2 x 2 x 2 x 2 x 179
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 32769888 = 2 x 2 x 2 x 2 x 2 x 3 x 179 x 1907
Step 4: Therefore, the least common multiple of 5721 and 5728 is 32769888.