Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 660 and 667 the smallest integer that is 440220 that is divisible by both numbers.
Least Common Multiple (LCM) of 660 and 667 is 440220.
LCM(660,667) = 440220
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 660 and 667. First we will calculate the prime factors of 660 and 667.
Prime Factorization of 660
2 | 660 |
2 | 330 |
3 | 165 |
5 | 55 |
11 | 11 |
1 |
Prime factors of 660 are 2, 3, 5,11. Prime factorization of 660 in exponential form is:
660 = 22×31×51×111
Prime Factorization of 667
23 | 667 |
29 | 29 |
1 |
Prime factors of 667 are 23,29. Prime factorization of 667 in exponential form is:
667 = 231×291
Now multiplying the highest exponent prime factors to calculate the LCM of 660 and 667.
LCM(660,667) = 22×31×51×111×231×291
LCM(660,667) = 440220
Factors of 660
List of positive integer factors of 660 that divides 660 without a remainder.
1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
Factors of 667
List of positive integer factors of 667 that divides 667 without a remainder.
1, 23, 29, 667
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 660 and 667, than apply into the LCM equation.
GCF(660,667) = 1
LCM(660,667) = ( 660 × 667) / 1
LCM(660,667) = 440220 / 1
LCM(660,667) = 440220
(i) The LCM of 667 and 660 is associative
LCM of 660 and 667 = LCM of 667 and 660
1. What is the LCM of 660 and 667?
Answer: LCM of 660 and 667 is 440220.
2. What are the Factors of 660?
Answer: Factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660. There are 24 integers that are factors of 660. The greatest factor of 660 is 660.
3. What are the Factors of 667?
Answer: Factors of 667 are 1, 23, 29, 667. There are 4 integers that are factors of 667. The greatest factor of 667 is 667.
4. How to Find the LCM of 660 and 667?
Answer:
Least Common Multiple of 660 and 667 = 440220
Step 1: Find the prime factorization of 660
660 = 2 x 2 x 3 x 5 x 11
Step 2: Find the prime factorization of 667
667 = 23 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 440220 = 2 x 2 x 3 x 5 x 11 x 23 x 29
Step 4: Therefore, the least common multiple of 660 and 667 is 440220.