Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 5 and 17 the smallest integer that is 85 that is divisible by both numbers.
Least Common Multiple (LCM) of 5 and 17 is 85.
LCM(5,17) = 85
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 5 and 17. First we will calculate the prime factors of 5 and 17.
Prime Factorization of 5
5 | 5 |
1 |
Prime factors of 5 are 5. Prime factorization of 5 in exponential form is:
5 = 51
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 5 and 17.
LCM(5,17) = 51×171
LCM(5,17) = 85
Factors of 5
List of positive integer factors of 5 that divides 5 without a remainder.
1, 5
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 5 and 17, than apply into the LCM equation.
GCF(5,17) = 1
LCM(5,17) = ( 5 × 17) / 1
LCM(5,17) = 85 / 1
LCM(5,17) = 85
(i) The LCM of 17 and 5 is associative
LCM of 5 and 17 = LCM of 17 and 5
1. What is the LCM of 5 and 17?
Answer: LCM of 5 and 17 is 85.
2. What are the Factors of 5?
Answer: Factors of 5 are 1, 5. There are 2 integers that are factors of 5. The greatest factor of 5 is 5.
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 5 and 17?
Answer:
Least Common Multiple of 5 and 17 = 85
Step 1: Find the prime factorization of 5
5 = 5
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 = 85 = 5 x 17
Step 4: Therefore, the least common multiple of 5 and 17 is 85.