Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 658 and 663 the smallest integer that is 436254 that is divisible by both numbers.
Least Common Multiple (LCM) of 658 and 663 is 436254.
LCM(658,663) = 436254
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 658 and 663. First we will calculate the prime factors of 658 and 663.
Prime Factorization of 658
2 | 658 |
7 | 329 |
47 | 47 |
1 |
Prime factors of 658 are 2, 7,47. Prime factorization of 658 in exponential form is:
658 = 21×71×471
Prime Factorization of 663
3 | 663 |
13 | 221 |
17 | 17 |
1 |
Prime factors of 663 are 3, 13,17. Prime factorization of 663 in exponential form is:
663 = 31×131×171
Now multiplying the highest exponent prime factors to calculate the LCM of 658 and 663.
LCM(658,663) = 21×31×71×131×171×471
LCM(658,663) = 436254
Factors of 658
List of positive integer factors of 658 that divides 658 without a remainder.
1, 2, 7, 14, 47, 94, 329, 658
Factors of 663
List of positive integer factors of 663 that divides 663 without a remainder.
1, 3, 13, 17, 39, 51, 221, 663
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 658 and 663, than apply into the LCM equation.
GCF(658,663) = 1
LCM(658,663) = ( 658 × 663) / 1
LCM(658,663) = 436254 / 1
LCM(658,663) = 436254
(i) The LCM of 663 and 658 is associative
LCM of 658 and 663 = LCM of 663 and 658
1. What is the LCM of 658 and 663?
Answer: LCM of 658 and 663 is 436254.
2. What are the Factors of 658?
Answer: Factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658. There are 8 integers that are factors of 658. The greatest factor of 658 is 658.
3. What are the Factors of 663?
Answer: Factors of 663 are 1, 3, 13, 17, 39, 51, 221, 663. There are 8 integers that are factors of 663. The greatest factor of 663 is 663.
4. How to Find the LCM of 658 and 663?
Answer:
Least Common Multiple of 658 and 663 = 436254
Step 1: Find the prime factorization of 658
658 = 2 x 7 x 47
Step 2: Find the prime factorization of 663
663 = 3 x 13 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 436254 = 2 x 3 x 7 x 13 x 17 x 47
Step 4: Therefore, the least common multiple of 658 and 663 is 436254.