Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2782 and 2787 the smallest integer that is 7753434 that is divisible by both numbers.
Least Common Multiple (LCM) of 2782 and 2787 is 7753434.
LCM(2782,2787) = 7753434
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 2782 and 2787. First we will calculate the prime factors of 2782 and 2787.
Prime Factorization of 2782
2 | 2782 |
13 | 1391 |
107 | 107 |
1 |
Prime factors of 2782 are 2, 13,107. Prime factorization of 2782 in exponential form is:
2782 = 21×131×1071
Prime Factorization of 2787
3 | 2787 |
929 | 929 |
1 |
Prime factors of 2787 are 3,929. Prime factorization of 2787 in exponential form is:
2787 = 31×9291
Now multiplying the highest exponent prime factors to calculate the LCM of 2782 and 2787.
LCM(2782,2787) = 21×31×131×1071×9291
LCM(2782,2787) = 7753434
Factors of 2782
List of positive integer factors of 2782 that divides 2782 without a remainder.
1, 2, 13, 26, 107, 214, 1391, 2782
Factors of 2787
List of positive integer factors of 2787 that divides 2787 without a remainder.
1, 3, 929, 2787
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2782 and 2787, than apply into the LCM equation.
GCF(2782,2787) = 1
LCM(2782,2787) = ( 2782 × 2787) / 1
LCM(2782,2787) = 7753434 / 1
LCM(2782,2787) = 7753434
(i) The LCM of 2787 and 2782 is associative
LCM of 2782 and 2787 = LCM of 2787 and 2782
1. What is the LCM of 2782 and 2787?
Answer: LCM of 2782 and 2787 is 7753434.
2. What are the Factors of 2782?
Answer: Factors of 2782 are 1, 2, 13, 26, 107, 214, 1391, 2782. There are 8 integers that are factors of 2782. The greatest factor of 2782 is 2782.
3. What are the Factors of 2787?
Answer: Factors of 2787 are 1, 3, 929, 2787. There are 4 integers that are factors of 2787. The greatest factor of 2787 is 2787.
4. How to Find the LCM of 2782 and 2787?
Answer:
Least Common Multiple of 2782 and 2787 = 7753434
Step 1: Find the prime factorization of 2782
2782 = 2 x 13 x 107
Step 2: Find the prime factorization of 2787
2787 = 3 x 929
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7753434 = 2 x 3 x 13 x 107 x 929
Step 4: Therefore, the least common multiple of 2782 and 2787 is 7753434.