Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 45 and 65 the smallest integer that is 585 that is divisible by both numbers.
Least Common Multiple (LCM) of 45 and 65 is 585.
LCM(45,65) = 585
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 45 and 65. First we will calculate the prime factors of 45 and 65.
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
Prime Factorization of 65
5 | 65 |
13 | 13 |
1 |
Prime factors of 65 are 5,13. Prime factorization of 65 in exponential form is:
65 = 51×131
Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 65.
LCM(45,65) = 32×51×131
LCM(45,65) = 585
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1, 3, 5, 9, 15, 45
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1, 5, 13, 65
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45 and 65, than apply into the LCM equation.
GCF(45,65) = 5
LCM(45,65) = ( 45 × 65) / 5
LCM(45,65) = 2925 / 5
LCM(45,65) = 585
(i) The LCM of 65 and 45 is associative
LCM of 45 and 65 = LCM of 65 and 45
1. What is the LCM of 45 and 65?
Answer: LCM of 45 and 65 is 585.
2. 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.
3. What are the Factors of 65?
Answer: Factors of 65 are 1, 5, 13, 65. There are 4 integers that are factors of 65. The greatest factor of 65 is 65.
4. How to Find the LCM of 45 and 65?
Answer:
Least Common Multiple of 45 and 65 = 585
Step 1: Find the prime factorization of 45
45 = 3 x 3 x 5
Step 2: Find the prime factorization of 65
65 = 5 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 585 = 3 x 3 x 5 x 13
Step 4: Therefore, the least common multiple of 45 and 65 is 585.