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 17 the smallest integer that is 102 that is divisible by both numbers.
Least Common Multiple (LCM) of 6 and 17 is 102.
LCM(6,17) = 102
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 17. First we will calculate the prime factors of 6 and 17.
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 17
17 | 17 |
1 |
Prime factors of 17 are 17. Prime factorization of 17 in exponential form is:
17 = 171
Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 17.
LCM(6,17) = 21×31×171
LCM(6,17) = 102
Factors of 6
List of positive integer factors of 6 that divides 6 without a remainder.
1, 2, 3, 6
Factors of 17
List of positive integer factors of 17 that divides 17 without a remainder.
1, 17
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 17, than apply into the LCM equation.
GCF(6,17) = 1
LCM(6,17) = ( 6 × 17) / 1
LCM(6,17) = 102 / 1
LCM(6,17) = 102
(i) The LCM of 17 and 6 is associative
LCM of 6 and 17 = LCM of 17 and 6
1. What is the LCM of 6 and 17?
Answer: LCM of 6 and 17 is 102.
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 17?
Answer: Factors of 17 are 1, 17. There are 2 integers that are factors of 17. The greatest factor of 17 is 17.
4. How to Find the LCM of 6 and 17?
Answer:
Least Common Multiple of 6 and 17 = 102
Step 1: Find the prime factorization of 6
6 = 2 x 3
Step 2: Find the prime factorization of 17
17 = 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 102 = 2 x 3 x 17
Step 4: Therefore, the least common multiple of 6 and 17 is 102.