Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1040 and 1045 the smallest integer that is 217360 that is divisible by both numbers.
Least Common Multiple (LCM) of 1040 and 1045 is 217360.
LCM(1040,1045) = 217360
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 1040 and 1045. First we will calculate the prime factors of 1040 and 1045.
Prime Factorization of 1040
2 | 1040 |
2 | 520 |
2 | 260 |
2 | 130 |
5 | 65 |
13 | 13 |
1 |
Prime factors of 1040 are 2, 5,13. Prime factorization of 1040 in exponential form is:
1040 = 24×51×131
Prime Factorization of 1045
5 | 1045 |
11 | 209 |
19 | 19 |
1 |
Prime factors of 1045 are 5, 11,19. Prime factorization of 1045 in exponential form is:
1045 = 51×111×191
Now multiplying the highest exponent prime factors to calculate the LCM of 1040 and 1045.
LCM(1040,1045) = 24×51×111×131×191
LCM(1040,1045) = 217360
Factors of 1040
List of positive integer factors of 1040 that divides 1040 without a remainder.
1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 40, 52, 65, 80, 104, 130, 208, 260, 520, 1040
Factors of 1045
List of positive integer factors of 1045 that divides 1045 without a remainder.
1, 5, 11, 19, 55, 95, 209, 1045
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1040 and 1045, than apply into the LCM equation.
GCF(1040,1045) = 5
LCM(1040,1045) = ( 1040 × 1045) / 5
LCM(1040,1045) = 1086800 / 5
LCM(1040,1045) = 217360
(i) The LCM of 1045 and 1040 is associative
LCM of 1040 and 1045 = LCM of 1045 and 1040
1. What is the LCM of 1040 and 1045?
Answer: LCM of 1040 and 1045 is 217360.
2. What are the Factors of 1040?
Answer: Factors of 1040 are 1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 40, 52, 65, 80, 104, 130, 208, 260, 520, 1040. There are 20 integers that are factors of 1040. The greatest factor of 1040 is 1040.
3. What are the Factors of 1045?
Answer: Factors of 1045 are 1, 5, 11, 19, 55, 95, 209, 1045. There are 8 integers that are factors of 1045. The greatest factor of 1045 is 1045.
4. How to Find the LCM of 1040 and 1045?
Answer:
Least Common Multiple of 1040 and 1045 = 217360
Step 1: Find the prime factorization of 1040
1040 = 2 x 2 x 2 x 2 x 5 x 13
Step 2: Find the prime factorization of 1045
1045 = 5 x 11 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 217360 = 2 x 2 x 2 x 2 x 5 x 11 x 13 x 19
Step 4: Therefore, the least common multiple of 1040 and 1045 is 217360.