Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1687 and 1691 the smallest integer that is 2852717 that is divisible by both numbers.
Least Common Multiple (LCM) of 1687 and 1691 is 2852717.
LCM(1687,1691) = 2852717
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 1687 and 1691. First we will calculate the prime factors of 1687 and 1691.
Prime Factorization of 1687
7 | 1687 |
241 | 241 |
1 |
Prime factors of 1687 are 7,241. Prime factorization of 1687 in exponential form is:
1687 = 71×2411
Prime Factorization of 1691
19 | 1691 |
89 | 89 |
1 |
Prime factors of 1691 are 19,89. Prime factorization of 1691 in exponential form is:
1691 = 191×891
Now multiplying the highest exponent prime factors to calculate the LCM of 1687 and 1691.
LCM(1687,1691) = 71×191×891×2411
LCM(1687,1691) = 2852717
Factors of 1687
List of positive integer factors of 1687 that divides 1687 without a remainder.
1, 7, 241, 1687
Factors of 1691
List of positive integer factors of 1691 that divides 1691 without a remainder.
1, 19, 89, 1691
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1687 and 1691, than apply into the LCM equation.
GCF(1687,1691) = 1
LCM(1687,1691) = ( 1687 × 1691) / 1
LCM(1687,1691) = 2852717 / 1
LCM(1687,1691) = 2852717
(i) The LCM of 1691 and 1687 is associative
LCM of 1687 and 1691 = LCM of 1691 and 1687
1. What is the LCM of 1687 and 1691?
Answer: LCM of 1687 and 1691 is 2852717.
2. What are the Factors of 1687?
Answer: Factors of 1687 are 1, 7, 241, 1687. There are 4 integers that are factors of 1687. The greatest factor of 1687 is 1687.
3. What are the Factors of 1691?
Answer: Factors of 1691 are 1, 19, 89, 1691. There are 4 integers that are factors of 1691. The greatest factor of 1691 is 1691.
4. How to Find the LCM of 1687 and 1691?
Answer:
Least Common Multiple of 1687 and 1691 = 2852717
Step 1: Find the prime factorization of 1687
1687 = 7 x 241
Step 2: Find the prime factorization of 1691
1691 = 19 x 89
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2852717 = 7 x 19 x 89 x 241
Step 4: Therefore, the least common multiple of 1687 and 1691 is 2852717.