Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2716 and 2724 the smallest integer that is 1849596 that is divisible by both numbers.
Least Common Multiple (LCM) of 2716 and 2724 is 1849596.
LCM(2716,2724) = 1849596
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 2716 and 2724. First we will calculate the prime factors of 2716 and 2724.
Prime Factorization of 2716
2 | 2716 |
2 | 1358 |
7 | 679 |
97 | 97 |
1 |
Prime factors of 2716 are 2, 7,97. Prime factorization of 2716 in exponential form is:
2716 = 22×71×971
Prime Factorization of 2724
2 | 2724 |
2 | 1362 |
3 | 681 |
227 | 227 |
1 |
Prime factors of 2724 are 2, 3,227. Prime factorization of 2724 in exponential form is:
2724 = 22×31×2271
Now multiplying the highest exponent prime factors to calculate the LCM of 2716 and 2724.
LCM(2716,2724) = 22×31×71×971×2271
LCM(2716,2724) = 1849596
Factors of 2716
List of positive integer factors of 2716 that divides 2716 without a remainder.
1, 2, 4, 7, 14, 28, 97, 194, 388, 679, 1358, 2716
Factors of 2724
List of positive integer factors of 2724 that divides 2724 without a remainder.
1, 2, 3, 4, 6, 12, 227, 454, 681, 908, 1362, 2724
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2716 and 2724, than apply into the LCM equation.
GCF(2716,2724) = 4
LCM(2716,2724) = ( 2716 × 2724) / 4
LCM(2716,2724) = 7398384 / 4
LCM(2716,2724) = 1849596
(i) The LCM of 2724 and 2716 is associative
LCM of 2716 and 2724 = LCM of 2724 and 2716
1. What is the LCM of 2716 and 2724?
Answer: LCM of 2716 and 2724 is 1849596.
2. What are the Factors of 2716?
Answer: Factors of 2716 are 1, 2, 4, 7, 14, 28, 97, 194, 388, 679, 1358, 2716. There are 12 integers that are factors of 2716. The greatest factor of 2716 is 2716.
3. What are the Factors of 2724?
Answer: Factors of 2724 are 1, 2, 3, 4, 6, 12, 227, 454, 681, 908, 1362, 2724. There are 12 integers that are factors of 2724. The greatest factor of 2724 is 2724.
4. How to Find the LCM of 2716 and 2724?
Answer:
Least Common Multiple of 2716 and 2724 = 1849596
Step 1: Find the prime factorization of 2716
2716 = 2 x 2 x 7 x 97
Step 2: Find the prime factorization of 2724
2724 = 2 x 2 x 3 x 227
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1849596 = 2 x 2 x 3 x 7 x 97 x 227
Step 4: Therefore, the least common multiple of 2716 and 2724 is 1849596.