Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1805 and 1812 the smallest integer that is 3270660 that is divisible by both numbers.
Least Common Multiple (LCM) of 1805 and 1812 is 3270660.
LCM(1805,1812) = 3270660
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 1805 and 1812. First we will calculate the prime factors of 1805 and 1812.
Prime Factorization of 1805
5 | 1805 |
19 | 361 |
19 | 19 |
1 |
Prime factors of 1805 are 5,19. Prime factorization of 1805 in exponential form is:
1805 = 51×192
Prime Factorization of 1812
2 | 1812 |
2 | 906 |
3 | 453 |
151 | 151 |
1 |
Prime factors of 1812 are 2, 3,151. Prime factorization of 1812 in exponential form is:
1812 = 22×31×1511
Now multiplying the highest exponent prime factors to calculate the LCM of 1805 and 1812.
LCM(1805,1812) = 22×31×51×192×1511
LCM(1805,1812) = 3270660
Factors of 1805
List of positive integer factors of 1805 that divides 1805 without a remainder.
1, 5, 19, 95, 361, 1805
Factors of 1812
List of positive integer factors of 1812 that divides 1812 without a remainder.
1, 2, 3, 4, 6, 12, 151, 302, 453, 604, 906, 1812
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1805 and 1812, than apply into the LCM equation.
GCF(1805,1812) = 1
LCM(1805,1812) = ( 1805 × 1812) / 1
LCM(1805,1812) = 3270660 / 1
LCM(1805,1812) = 3270660
(i) The LCM of 1812 and 1805 is associative
LCM of 1805 and 1812 = LCM of 1812 and 1805
1. What is the LCM of 1805 and 1812?
Answer: LCM of 1805 and 1812 is 3270660.
2. What are the Factors of 1805?
Answer: Factors of 1805 are 1, 5, 19, 95, 361, 1805. There are 6 integers that are factors of 1805. The greatest factor of 1805 is 1805.
3. What are the Factors of 1812?
Answer: Factors of 1812 are 1, 2, 3, 4, 6, 12, 151, 302, 453, 604, 906, 1812. There are 12 integers that are factors of 1812. The greatest factor of 1812 is 1812.
4. How to Find the LCM of 1805 and 1812?
Answer:
Least Common Multiple of 1805 and 1812 = 3270660
Step 1: Find the prime factorization of 1805
1805 = 5 x 19 x 19
Step 2: Find the prime factorization of 1812
1812 = 2 x 2 x 3 x 151
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3270660 = 2 x 2 x 3 x 5 x 19 x 19 x 151
Step 4: Therefore, the least common multiple of 1805 and 1812 is 3270660.