Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1036 and 1042 the smallest integer that is 539756 that is divisible by both numbers.
Least Common Multiple (LCM) of 1036 and 1042 is 539756.
LCM(1036,1042) = 539756
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 1036 and 1042. First we will calculate the prime factors of 1036 and 1042.
Prime Factorization of 1036
2 | 1036 |
2 | 518 |
7 | 259 |
37 | 37 |
1 |
Prime factors of 1036 are 2, 7,37. Prime factorization of 1036 in exponential form is:
1036 = 22×71×371
Prime Factorization of 1042
2 | 1042 |
521 | 521 |
1 |
Prime factors of 1042 are 2,521. Prime factorization of 1042 in exponential form is:
1042 = 21×5211
Now multiplying the highest exponent prime factors to calculate the LCM of 1036 and 1042.
LCM(1036,1042) = 22×71×371×5211
LCM(1036,1042) = 539756
Factors of 1036
List of positive integer factors of 1036 that divides 1036 without a remainder.
1, 2, 4, 7, 14, 28, 37, 74, 148, 259, 518, 1036
Factors of 1042
List of positive integer factors of 1042 that divides 1042 without a remainder.
1, 2, 521, 1042
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1036 and 1042, than apply into the LCM equation.
GCF(1036,1042) = 2
LCM(1036,1042) = ( 1036 × 1042) / 2
LCM(1036,1042) = 1079512 / 2
LCM(1036,1042) = 539756
(i) The LCM of 1042 and 1036 is associative
LCM of 1036 and 1042 = LCM of 1042 and 1036
1. What is the LCM of 1036 and 1042?
Answer: LCM of 1036 and 1042 is 539756.
2. What are the Factors of 1036?
Answer: Factors of 1036 are 1, 2, 4, 7, 14, 28, 37, 74, 148, 259, 518, 1036. There are 12 integers that are factors of 1036. The greatest factor of 1036 is 1036.
3. What are the Factors of 1042?
Answer: Factors of 1042 are 1, 2, 521, 1042. There are 4 integers that are factors of 1042. The greatest factor of 1042 is 1042.
4. How to Find the LCM of 1036 and 1042?
Answer:
Least Common Multiple of 1036 and 1042 = 539756
Step 1: Find the prime factorization of 1036
1036 = 2 x 2 x 7 x 37
Step 2: Find the prime factorization of 1042
1042 = 2 x 521
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 539756 = 2 x 2 x 7 x 37 x 521
Step 4: Therefore, the least common multiple of 1036 and 1042 is 539756.