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 668 the smallest integer that is 110220 that is divisible by both numbers.
Least Common Multiple (LCM) of 660 and 668 is 110220.
LCM(660,668) = 110220
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 668. First we will calculate the prime factors of 660 and 668.
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 668
2 | 668 |
2 | 334 |
167 | 167 |
1 |
Prime factors of 668 are 2,167. Prime factorization of 668 in exponential form is:
668 = 22×1671
Now multiplying the highest exponent prime factors to calculate the LCM of 660 and 668.
LCM(660,668) = 22×31×51×111×1671
LCM(660,668) = 110220
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 668
List of positive integer factors of 668 that divides 668 without a remainder.
1, 2, 4, 167, 334, 668
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 660 and 668, than apply into the LCM equation.
GCF(660,668) = 4
LCM(660,668) = ( 660 × 668) / 4
LCM(660,668) = 440880 / 4
LCM(660,668) = 110220
(i) The LCM of 668 and 660 is associative
LCM of 660 and 668 = LCM of 668 and 660
1. What is the LCM of 660 and 668?
Answer: LCM of 660 and 668 is 110220.
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 668?
Answer: Factors of 668 are 1, 2, 4, 167, 334, 668. There are 6 integers that are factors of 668. The greatest factor of 668 is 668.
4. How to Find the LCM of 660 and 668?
Answer:
Least Common Multiple of 660 and 668 = 110220
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 668
668 = 2 x 2 x 167
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 110220 = 2 x 2 x 3 x 5 x 11 x 167
Step 4: Therefore, the least common multiple of 660 and 668 is 110220.