Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8 and 17 the smallest integer that is 136 that is divisible by both numbers.
Least Common Multiple (LCM) of 8 and 17 is 136.
LCM(8,17) = 136
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 8 and 17. First we will calculate the prime factors of 8 and 17.
Prime Factorization of 8
2 | 8 |
2 | 4 |
2 | 2 |
1 |
Prime factors of 8 are 2. Prime factorization of 8 in exponential form is:
8 = 23
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 8 and 17.
LCM(8,17) = 23×171
LCM(8,17) = 136
Factors of 8
List of positive integer factors of 8 that divides 8 without a remainder.
1, 2, 4, 8
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 8 and 17, than apply into the LCM equation.
GCF(8,17) = 1
LCM(8,17) = ( 8 × 17) / 1
LCM(8,17) = 136 / 1
LCM(8,17) = 136
(i) The LCM of 17 and 8 is associative
LCM of 8 and 17 = LCM of 17 and 8
1. What is the LCM of 8 and 17?
Answer: LCM of 8 and 17 is 136.
2. What are the Factors of 8?
Answer: Factors of 8 are 1, 2, 4, 8. There are 4 integers that are factors of 8. The greatest factor of 8 is 8.
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 8 and 17?
Answer:
Least Common Multiple of 8 and 17 = 136
Step 1: Find the prime factorization of 8
8 = 2 x 2 x 2
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 = 136 = 2 x 2 x 2 x 17
Step 4: Therefore, the least common multiple of 8 and 17 is 136.