Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6 and 9 the smallest integer that is 18 that is divisible by both numbers.
Least Common Multiple (LCM) of 6 and 9 is 18.
LCM(6,9) = 18
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 6 and 9. First we will calculate the prime factors of 6 and 9.
Prime Factorization of 6
2 | 6 |
3 | 3 |
1 |
Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:
6 = 21×31
Prime Factorization of 9
3 | 9 |
3 | 3 |
1 |
Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:
9 = 32
Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 9.
LCM(6,9) = 21×32
LCM(6,9) = 18
Factors of 6
List of positive integer factors of 6 that divides 6 without a remainder.
1, 2, 3, 6
Factors of 9
List of positive integer factors of 9 that divides 9 without a remainder.
1, 3, 9
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 9, than apply into the LCM equation.
GCF(6,9) = 3
LCM(6,9) = ( 6 × 9) / 3
LCM(6,9) = 54 / 3
LCM(6,9) = 18
(i) The LCM of 9 and 6 is associative
LCM of 6 and 9 = LCM of 9 and 6
1. What is the LCM of 6 and 9?
Answer: LCM of 6 and 9 is 18.
2. What are the Factors of 6?
Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.
3. What are the Factors of 9?
Answer: Factors of 9 are 1, 3, 9. There are 3 integers that are factors of 9. The greatest factor of 9 is 9.
4. How to Find the LCM of 6 and 9?
Answer:
Least Common Multiple of 6 and 9 = 18
Step 1: Find the prime factorization of 6
6 = 2 x 3
Step 2: Find the prime factorization of 9
9 = 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 18 = 2 x 3 x 3
Step 4: Therefore, the least common multiple of 6 and 9 is 18.