Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1074 and 1076 the smallest integer that is 577812 that is divisible by both numbers.
Least Common Multiple (LCM) of 1074 and 1076 is 577812.
LCM(1074,1076) = 577812
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 1074 and 1076. First we will calculate the prime factors of 1074 and 1076.
Prime Factorization of 1074
2 | 1074 |
3 | 537 |
179 | 179 |
1 |
Prime factors of 1074 are 2, 3,179. Prime factorization of 1074 in exponential form is:
1074 = 21×31×1791
Prime Factorization of 1076
2 | 1076 |
2 | 538 |
269 | 269 |
1 |
Prime factors of 1076 are 2,269. Prime factorization of 1076 in exponential form is:
1076 = 22×2691
Now multiplying the highest exponent prime factors to calculate the LCM of 1074 and 1076.
LCM(1074,1076) = 22×31×1791×2691
LCM(1074,1076) = 577812
Factors of 1074
List of positive integer factors of 1074 that divides 1074 without a remainder.
1, 2, 3, 6, 179, 358, 537, 1074
Factors of 1076
List of positive integer factors of 1076 that divides 1076 without a remainder.
1, 2, 4, 269, 538, 1076
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1074 and 1076, than apply into the LCM equation.
GCF(1074,1076) = 2
LCM(1074,1076) = ( 1074 × 1076) / 2
LCM(1074,1076) = 1155624 / 2
LCM(1074,1076) = 577812
(i) The LCM of 1076 and 1074 is associative
LCM of 1074 and 1076 = LCM of 1076 and 1074
1. What is the LCM of 1074 and 1076?
Answer: LCM of 1074 and 1076 is 577812.
2. What are the Factors of 1074?
Answer: Factors of 1074 are 1, 2, 3, 6, 179, 358, 537, 1074. There are 8 integers that are factors of 1074. The greatest factor of 1074 is 1074.
3. What are the Factors of 1076?
Answer: Factors of 1076 are 1, 2, 4, 269, 538, 1076. There are 6 integers that are factors of 1076. The greatest factor of 1076 is 1076.
4. How to Find the LCM of 1074 and 1076?
Answer:
Least Common Multiple of 1074 and 1076 = 577812
Step 1: Find the prime factorization of 1074
1074 = 2 x 3 x 179
Step 2: Find the prime factorization of 1076
1076 = 2 x 2 x 269
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 577812 = 2 x 2 x 3 x 179 x 269
Step 4: Therefore, the least common multiple of 1074 and 1076 is 577812.