Least Common Multiple of 10 and 18
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 10 and 18 the smallest integer that is 90 that is divisible by both numbers.
Least Common Multiple (LCM) of 10 and 18 is 90.
LCM(10,18) = 90
LCM of 10 and 18
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 10 and 18 by Prime method
- Least Common Multiple of 10 and 18 with GCF Formula
LCM of 10 and 18 is 90
Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 18. First we will calculate the prime factors of 10 and 18.
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
Prime Factorization of 18
| 2 | 18 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:
18 = 21×32
Now multiplying the highest exponent prime factors to calculate the LCM of 10 and 18.
LCM(10,18) = 21×32×51
LCM(10,18) = 90
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1, 2, 5, 10
Factors of 18
List of positive integer factors of 18 that divides 18 without a remainder.
1, 2, 3, 6, 9, 18
Least Common Multiple of 10 and 18 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10 and 18, than apply into the LCM equation.
GCF(10,18) = 2
LCM(10,18) = ( 10 × 18) / 2
LCM(10,18) = 180 / 2
LCM(10,18) = 90
Properties of LCM 10 and 18
(i) The LCM of 18 and 10 is associative
LCM of 10 and 18 = LCM of 18 and 10
Related Least Common Multiples of 10
Related Least Common Multiples of 18
Frequently Asked Questions on LCM of 10 and 18
1. What is the LCM of 10 and 18?
Answer: LCM of 10 and 18 is 90.
2. 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.
3. What are the Factors of 18?
Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.
4. How to Find the LCM of 10 and 18?
Answer:
Least Common Multiple of 10 and 18 = 90
Step 1: Find the prime factorization of 10
10 = 2 x 5
Step 2: Find the prime factorization of 18
18 = 2 x 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 = 90 = 2 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 10 and 18 is 90.
