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 663 the smallest integer that is 145860 that is divisible by both numbers.
Least Common Multiple (LCM) of 660 and 663 is 145860.
LCM(660,663) = 145860
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 663. First we will calculate the prime factors of 660 and 663.
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 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 660 and 663.
LCM(660,663) = 22×31×51×111×131×171
LCM(660,663) = 145860
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 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 660 and 663, than apply into the LCM equation.
GCF(660,663) = 3
LCM(660,663) = ( 660 × 663) / 3
LCM(660,663) = 437580 / 3
LCM(660,663) = 145860
(i) The LCM of 663 and 660 is associative
LCM of 660 and 663 = LCM of 663 and 660
1. What is the LCM of 660 and 663?
Answer: LCM of 660 and 663 is 145860.
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 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 660 and 663?
Answer:
Least Common Multiple of 660 and 663 = 145860
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 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 = 145860 = 2 x 2 x 3 x 5 x 11 x 13 x 17
Step 4: Therefore, the least common multiple of 660 and 663 is 145860.