LCM of 85 and 90
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 85 and 90 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 1530 as output. Here you can check the answer for Find the LCM of 85 and 90.
What is LCM of 85 and 90
Given Numbers are 85, 90
We can find the LCM of 85, 90 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 85 and 90
Multiples of 85 =85,170,255,340,425,510,595,680,765,850,935,1020,1105,1190,1275,1360,1445,
Multiples of 90 =90,180,270,360,450,540,630,720,810,900,990,1080,1170,1260,1350,1440,1530,
Now, get the least common multiple of 85, 90 which is 1530
So, the LCM of 85, 90 is 1530.
Least Common Multiple (LCM) of 85 and 90 with the help of Prime Factorisation
One method for determining the LCM of 85 and 90 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 85's prime factorization:
| 5 | 85 |
| 17 | 17 |
| 1 |
Prime factors of 85 are 5,17.
85 = 51×171
And this is 90's prime factorization:
| 2 | 90 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 90 are 2, 3,5.
90 = 21×32×51
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 5,17, 2,3
.21×32×51×171 = 1530
This shows that the LCM of 85 and 90 is 1530.
How to Calculate the LCM of 85 and 90 Using Common Multiples
The first step in determining the Least Common Multiple of 85 and 90 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 85 and 90:
Lets look at the first ten multiples of these numbers, 85 and 90:
85,170,255,340,425,510,595,680,765,1445 are the first ten multiples of 85.
90,180,270,360,450,540,630,720,810,1530 are the first ten multiples of 90.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 85 and 90, for example, are 1020, 1445, and 1440. 1530 is the least common multiple since it is the smallest.
85 and 90 have an LCM of 1530.
Least Common Multiple of 85 and 90 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85 and 90, than apply into the LCM equation.
GCF(85,90) = 5
LCM(85,90) = ( 85 × 90) / 5
LCM(85,90) = 7650 / 5
LCM(85,90) = 1530
Related Least Common Multiples of 85
Related Least Common Multiples of 90
Frequently Asked Questions on LCM of 85 and 90
1. What is the LCM of 85 and 90?
The LCM of 85 and 90 is 1530.
2. How to find the lowest common multiple of 85 and 90?
To find the lowest common multiple of 85 and 90, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1530.
3. What are the Factors of 85?
Answer: Factors of 85 are 1, 5, 17, 85. There are 4 integers that are factors of 85. The greatest factor of 85 is 85.
4. What are the Factors of 90?
Answer: Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. There are 12 integers that are factors of 90. The greatest factor of 90 is 90.
5. How to Find the LCM of 85 and 90?Answer:
Least Common Multiple of 85 and 90 = 1530
Step 1: Find the prime factorization of 85
85 = 5 x 17
Step 2: Find the prime factorization of 90
90 = 2 x 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 = 1530 = 2 x 3 x 3 x 5 x 17
Step 4: Therefore, the least common multiple of 85 and 90 is 1530.