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 9 the smallest integer that is 45 that is divisible by both numbers.
Least Common Multiple (LCM) of 5 and 9 is 45.
LCM(5,9) = 45
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 9. First we will calculate the prime factors of 5 and 9.
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 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 5 and 9.
LCM(5,9) = 32×51
LCM(5,9) = 45
Factors of 5
List of positive integer factors of 5 that divides 5 without a remainder.
1, 5
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 5 and 9, than apply into the LCM equation.
GCF(5,9) = 1
LCM(5,9) = ( 5 × 9) / 1
LCM(5,9) = 45 / 1
LCM(5,9) = 45
(i) The LCM of 9 and 5 is associative
LCM of 5 and 9 = LCM of 9 and 5
1. What is the LCM of 5 and 9?
Answer: LCM of 5 and 9 is 45.
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 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 5 and 9?
Answer:
Least Common Multiple of 5 and 9 = 45
Step 1: Find the prime factorization of 5
5 = 5
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 = 45 = 3 x 3 x 5
Step 4: Therefore, the least common multiple of 5 and 9 is 45.