Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2739 and 2744 the smallest integer that is 7515816 that is divisible by both numbers.
Least Common Multiple (LCM) of 2739 and 2744 is 7515816.
LCM(2739,2744) = 7515816
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 2739 and 2744. First we will calculate the prime factors of 2739 and 2744.
Prime Factorization of 2739
3 | 2739 |
11 | 913 |
83 | 83 |
1 |
Prime factors of 2739 are 3, 11,83. Prime factorization of 2739 in exponential form is:
2739 = 31×111×831
Prime Factorization of 2744
2 | 2744 |
2 | 1372 |
2 | 686 |
7 | 343 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 2744 are 2,7. Prime factorization of 2744 in exponential form is:
2744 = 23×73
Now multiplying the highest exponent prime factors to calculate the LCM of 2739 and 2744.
LCM(2739,2744) = 23×31×73×111×831
LCM(2739,2744) = 7515816
Factors of 2739
List of positive integer factors of 2739 that divides 2739 without a remainder.
1, 3, 11, 33, 83, 249, 913, 2739
Factors of 2744
List of positive integer factors of 2744 that divides 2744 without a remainder.
1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 343, 392, 686, 1372, 2744
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2739 and 2744, than apply into the LCM equation.
GCF(2739,2744) = 1
LCM(2739,2744) = ( 2739 × 2744) / 1
LCM(2739,2744) = 7515816 / 1
LCM(2739,2744) = 7515816
(i) The LCM of 2744 and 2739 is associative
LCM of 2739 and 2744 = LCM of 2744 and 2739
1. What is the LCM of 2739 and 2744?
Answer: LCM of 2739 and 2744 is 7515816.
2. What are the Factors of 2739?
Answer: Factors of 2739 are 1, 3, 11, 33, 83, 249, 913, 2739. There are 8 integers that are factors of 2739. The greatest factor of 2739 is 2739.
3. What are the Factors of 2744?
Answer: Factors of 2744 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 343, 392, 686, 1372, 2744. There are 16 integers that are factors of 2744. The greatest factor of 2744 is 2744.
4. How to Find the LCM of 2739 and 2744?
Answer:
Least Common Multiple of 2739 and 2744 = 7515816
Step 1: Find the prime factorization of 2739
2739 = 3 x 11 x 83
Step 2: Find the prime factorization of 2744
2744 = 2 x 2 x 2 x 7 x 7 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7515816 = 2 x 2 x 2 x 3 x 7 x 7 x 7 x 11 x 83
Step 4: Therefore, the least common multiple of 2739 and 2744 is 7515816.