Least Common Multiple of 27 and 45
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 27 and 45 the smallest integer that is 135 that is divisible by both numbers.
Least Common Multiple (LCM) of 27 and 45 is 135.
LCM(27,45) = 135
LCM of 27 and 45
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 27 and 45 by Prime method
- Least Common Multiple of 27 and 45 with GCF Formula
LCM of 27 and 45 is 135
Least common multiple can be found by multiplying the highest exponent prime factors of 27 and 45. First we will calculate the prime factors of 27 and 45.
Prime Factorization of 27
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:
27 = 33
Prime Factorization of 45
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 45 are 3,5. Prime factorization of 45 in exponential form is:
45 = 32×51
Now multiplying the highest exponent prime factors to calculate the LCM of 27 and 45.
LCM(27,45) = 33×51
LCM(27,45) = 135
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1, 3, 9, 27
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1, 3, 5, 9, 15, 45
Least Common Multiple of 27 and 45 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27 and 45, than apply into the LCM equation.
GCF(27,45) = 9
LCM(27,45) = ( 27 × 45) / 9
LCM(27,45) = 1215 / 9
LCM(27,45) = 135
Properties of LCM 27 and 45
(i) The LCM of 45 and 27 is associative
LCM of 27 and 45 = LCM of 45 and 27
Related Least Common Multiples of 27
Related Least Common Multiples of 45
Frequently Asked Questions on LCM of 27 and 45
1. What is the LCM of 27 and 45?
Answer: LCM of 27 and 45 is 135.
2. What are the Factors of 27?
Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.
3. What are the Factors of 45?
Answer: Factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 integers that are factors of 45. The greatest factor of 45 is 45.
4. How to Find the LCM of 27 and 45?
Answer:
Least Common Multiple of 27 and 45 = 135
Step 1: Find the prime factorization of 27
27 = 3 x 3 x 3
Step 2: Find the prime factorization of 45
45 = 3 x 3 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 = 135 = 3 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 27 and 45 is 135.
