Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 683 and 688 the smallest integer that is 469904 that is divisible by both numbers.
Least Common Multiple (LCM) of 683 and 688 is 469904.
LCM(683,688) = 469904
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 683 and 688. First we will calculate the prime factors of 683 and 688.
Prime Factorization of 683
683 | 683 |
1 |
Prime factors of 683 are 683. Prime factorization of 683 in exponential form is:
683 = 6831
Prime Factorization of 688
2 | 688 |
2 | 344 |
2 | 172 |
2 | 86 |
43 | 43 |
1 |
Prime factors of 688 are 2,43. Prime factorization of 688 in exponential form is:
688 = 24×431
Now multiplying the highest exponent prime factors to calculate the LCM of 683 and 688.
LCM(683,688) = 24×431×6831
LCM(683,688) = 469904
Factors of 683
List of positive integer factors of 683 that divides 683 without a remainder.
1, 683
Factors of 688
List of positive integer factors of 688 that divides 688 without a remainder.
1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 683 and 688, than apply into the LCM equation.
GCF(683,688) = 1
LCM(683,688) = ( 683 × 688) / 1
LCM(683,688) = 469904 / 1
LCM(683,688) = 469904
(i) The LCM of 688 and 683 is associative
LCM of 683 and 688 = LCM of 688 and 683
1. What is the LCM of 683 and 688?
Answer: LCM of 683 and 688 is 469904.
2. What are the Factors of 683?
Answer: Factors of 683 are 1, 683. There are 2 integers that are factors of 683. The greatest factor of 683 is 683.
3. What are the Factors of 688?
Answer: Factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688. There are 10 integers that are factors of 688. The greatest factor of 688 is 688.
4. How to Find the LCM of 683 and 688?
Answer:
Least Common Multiple of 683 and 688 = 469904
Step 1: Find the prime factorization of 683
683 = 683
Step 2: Find the prime factorization of 688
688 = 2 x 2 x 2 x 2 x 43
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 469904 = 2 x 2 x 2 x 2 x 43 x 683
Step 4: Therefore, the least common multiple of 683 and 688 is 469904.