Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2740 and 2745 the smallest integer that is 1504260 that is divisible by both numbers.
Least Common Multiple (LCM) of 2740 and 2745 is 1504260.
LCM(2740,2745) = 1504260
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 2740 and 2745. First we will calculate the prime factors of 2740 and 2745.
Prime Factorization of 2740
2 | 2740 |
2 | 1370 |
5 | 685 |
137 | 137 |
1 |
Prime factors of 2740 are 2, 5,137. Prime factorization of 2740 in exponential form is:
2740 = 22×51×1371
Prime Factorization of 2745
3 | 2745 |
3 | 915 |
5 | 305 |
61 | 61 |
1 |
Prime factors of 2745 are 3, 5,61. Prime factorization of 2745 in exponential form is:
2745 = 32×51×611
Now multiplying the highest exponent prime factors to calculate the LCM of 2740 and 2745.
LCM(2740,2745) = 22×32×51×611×1371
LCM(2740,2745) = 1504260
Factors of 2740
List of positive integer factors of 2740 that divides 2740 without a remainder.
1, 2, 4, 5, 10, 20, 137, 274, 548, 685, 1370, 2740
Factors of 2745
List of positive integer factors of 2745 that divides 2745 without a remainder.
1, 3, 5, 9, 15, 45, 61, 183, 305, 549, 915, 2745
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2740 and 2745, than apply into the LCM equation.
GCF(2740,2745) = 5
LCM(2740,2745) = ( 2740 × 2745) / 5
LCM(2740,2745) = 7521300 / 5
LCM(2740,2745) = 1504260
(i) The LCM of 2745 and 2740 is associative
LCM of 2740 and 2745 = LCM of 2745 and 2740
1. What is the LCM of 2740 and 2745?
Answer: LCM of 2740 and 2745 is 1504260.
2. What are the Factors of 2740?
Answer: Factors of 2740 are 1, 2, 4, 5, 10, 20, 137, 274, 548, 685, 1370, 2740. There are 12 integers that are factors of 2740. The greatest factor of 2740 is 2740.
3. What are the Factors of 2745?
Answer: Factors of 2745 are 1, 3, 5, 9, 15, 45, 61, 183, 305, 549, 915, 2745. There are 12 integers that are factors of 2745. The greatest factor of 2745 is 2745.
4. How to Find the LCM of 2740 and 2745?
Answer:
Least Common Multiple of 2740 and 2745 = 1504260
Step 1: Find the prime factorization of 2740
2740 = 2 x 2 x 5 x 137
Step 2: Find the prime factorization of 2745
2745 = 3 x 3 x 5 x 61
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1504260 = 2 x 2 x 3 x 3 x 5 x 61 x 137
Step 4: Therefore, the least common multiple of 2740 and 2745 is 1504260.