Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1684 and 1688 the smallest integer that is 710648 that is divisible by both numbers.
Least Common Multiple (LCM) of 1684 and 1688 is 710648.
LCM(1684,1688) = 710648
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 1684 and 1688. First we will calculate the prime factors of 1684 and 1688.
Prime Factorization of 1684
2 | 1684 |
2 | 842 |
421 | 421 |
1 |
Prime factors of 1684 are 2,421. Prime factorization of 1684 in exponential form is:
1684 = 22×4211
Prime Factorization of 1688
2 | 1688 |
2 | 844 |
2 | 422 |
211 | 211 |
1 |
Prime factors of 1688 are 2,211. Prime factorization of 1688 in exponential form is:
1688 = 23×2111
Now multiplying the highest exponent prime factors to calculate the LCM of 1684 and 1688.
LCM(1684,1688) = 23×2111×4211
LCM(1684,1688) = 710648
Factors of 1684
List of positive integer factors of 1684 that divides 1684 without a remainder.
1, 2, 4, 421, 842, 1684
Factors of 1688
List of positive integer factors of 1688 that divides 1688 without a remainder.
1, 2, 4, 8, 211, 422, 844, 1688
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1684 and 1688, than apply into the LCM equation.
GCF(1684,1688) = 4
LCM(1684,1688) = ( 1684 × 1688) / 4
LCM(1684,1688) = 2842592 / 4
LCM(1684,1688) = 710648
(i) The LCM of 1688 and 1684 is associative
LCM of 1684 and 1688 = LCM of 1688 and 1684
1. What is the LCM of 1684 and 1688?
Answer: LCM of 1684 and 1688 is 710648.
2. What are the Factors of 1684?
Answer: Factors of 1684 are 1, 2, 4, 421, 842, 1684. There are 6 integers that are factors of 1684. The greatest factor of 1684 is 1684.
3. What are the Factors of 1688?
Answer: Factors of 1688 are 1, 2, 4, 8, 211, 422, 844, 1688. There are 8 integers that are factors of 1688. The greatest factor of 1688 is 1688.
4. How to Find the LCM of 1684 and 1688?
Answer:
Least Common Multiple of 1684 and 1688 = 710648
Step 1: Find the prime factorization of 1684
1684 = 2 x 2 x 421
Step 2: Find the prime factorization of 1688
1688 = 2 x 2 x 2 x 211
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 710648 = 2 x 2 x 2 x 211 x 421
Step 4: Therefore, the least common multiple of 1684 and 1688 is 710648.