Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1785 and 1786 the smallest integer that is 3188010 that is divisible by both numbers.
Least Common Multiple (LCM) of 1785 and 1786 is 3188010.
LCM(1785,1786) = 3188010
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 1785 and 1786. First we will calculate the prime factors of 1785 and 1786.
Prime Factorization of 1785
3 | 1785 |
5 | 595 |
7 | 119 |
17 | 17 |
1 |
Prime factors of 1785 are 3, 5, 7,17. Prime factorization of 1785 in exponential form is:
1785 = 31×51×71×171
Prime Factorization of 1786
2 | 1786 |
19 | 893 |
47 | 47 |
1 |
Prime factors of 1786 are 2, 19,47. Prime factorization of 1786 in exponential form is:
1786 = 21×191×471
Now multiplying the highest exponent prime factors to calculate the LCM of 1785 and 1786.
LCM(1785,1786) = 21×31×51×71×171×191×471
LCM(1785,1786) = 3188010
Factors of 1785
List of positive integer factors of 1785 that divides 1785 without a remainder.
1, 3, 5, 7, 15, 17, 21, 35, 51, 85, 105, 119, 255, 357, 595, 1785
Factors of 1786
List of positive integer factors of 1786 that divides 1786 without a remainder.
1, 2, 19, 38, 47, 94, 893, 1786
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1785 and 1786, than apply into the LCM equation.
GCF(1785,1786) = 1
LCM(1785,1786) = ( 1785 × 1786) / 1
LCM(1785,1786) = 3188010 / 1
LCM(1785,1786) = 3188010
(i) The LCM of 1786 and 1785 is associative
LCM of 1785 and 1786 = LCM of 1786 and 1785
1. What is the LCM of 1785 and 1786?
Answer: LCM of 1785 and 1786 is 3188010.
2. What are the Factors of 1785?
Answer: Factors of 1785 are 1, 3, 5, 7, 15, 17, 21, 35, 51, 85, 105, 119, 255, 357, 595, 1785. There are 16 integers that are factors of 1785. The greatest factor of 1785 is 1785.
3. What are the Factors of 1786?
Answer: Factors of 1786 are 1, 2, 19, 38, 47, 94, 893, 1786. There are 8 integers that are factors of 1786. The greatest factor of 1786 is 1786.
4. How to Find the LCM of 1785 and 1786?
Answer:
Least Common Multiple of 1785 and 1786 = 3188010
Step 1: Find the prime factorization of 1785
1785 = 3 x 5 x 7 x 17
Step 2: Find the prime factorization of 1786
1786 = 2 x 19 x 47
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3188010 = 2 x 3 x 5 x 7 x 17 x 19 x 47
Step 4: Therefore, the least common multiple of 1785 and 1786 is 3188010.