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 666 the smallest integer that is 219114 that is divisible by both numbers.
Least Common Multiple (LCM) of 658 and 666 is 219114.
LCM(658,666) = 219114
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 666. First we will calculate the prime factors of 658 and 666.
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 666
2 | 666 |
3 | 333 |
3 | 111 |
37 | 37 |
1 |
Prime factors of 666 are 2, 3,37. Prime factorization of 666 in exponential form is:
666 = 21×32×371
Now multiplying the highest exponent prime factors to calculate the LCM of 658 and 666.
LCM(658,666) = 21×32×71×371×471
LCM(658,666) = 219114
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 666
List of positive integer factors of 666 that divides 666 without a remainder.
1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 658 and 666, than apply into the LCM equation.
GCF(658,666) = 2
LCM(658,666) = ( 658 × 666) / 2
LCM(658,666) = 438228 / 2
LCM(658,666) = 219114
(i) The LCM of 666 and 658 is associative
LCM of 658 and 666 = LCM of 666 and 658
1. What is the LCM of 658 and 666?
Answer: LCM of 658 and 666 is 219114.
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 666?
Answer: Factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666. There are 12 integers that are factors of 666. The greatest factor of 666 is 666.
4. How to Find the LCM of 658 and 666?
Answer:
Least Common Multiple of 658 and 666 = 219114
Step 1: Find the prime factorization of 658
658 = 2 x 7 x 47
Step 2: Find the prime factorization of 666
666 = 2 x 3 x 3 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 219114 = 2 x 3 x 3 x 7 x 37 x 47
Step 4: Therefore, the least common multiple of 658 and 666 is 219114.