Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 9 and 10 the smallest integer that is 90 that is divisible by both numbers.
Least Common Multiple (LCM) of 9 and 10 is 90.
LCM(9,10) = 90
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 9 and 10. First we will calculate the prime factors of 9 and 10.
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
Prime Factorization of 10
2 | 10 |
5 | 5 |
1 |
Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:
10 = 21×51
Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 10.
LCM(9,10) = 21×32×51
LCM(9,10) = 90
Factors of 9
List of positive integer factors of 9 that divides 9 without a remainder.
1, 3, 9
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1, 2, 5, 10
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 10, than apply into the LCM equation.
GCF(9,10) = 1
LCM(9,10) = ( 9 × 10) / 1
LCM(9,10) = 90 / 1
LCM(9,10) = 90
(i) The LCM of 10 and 9 is associative
LCM of 9 and 10 = LCM of 10 and 9
1. What is the LCM of 9 and 10?
Answer: LCM of 9 and 10 is 90.
2. 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.
3. What are the Factors of 10?
Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.
4. How to Find the LCM of 9 and 10?
Answer:
Least Common Multiple of 9 and 10 = 90
Step 1: Find the prime factorization of 9
9 = 3 x 3
Step 2: Find the prime factorization of 10
10 = 2 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 90 = 2 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 9 and 10 is 90.