LCM of 84 and 90
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 84 and 90 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 1260 as output. Here you can check the answer for Find the LCM of 84 and 90.
What is LCM of 84 and 90
Given Numbers are 84, 90
We can find the LCM of 84, 90 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 84 and 90
Multiples of 84 =84,168,252,336,420,504,588,672,756,840,924,1008,1092,1176,1260,1344,1428,
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 84, 90 which is 1260
So, the LCM of 84, 90 is 1260.
Least Common Multiple (LCM) of 84 and 90 with the help of Prime Factorisation
One method for determining the LCM of 84 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 84's prime factorization:
| 2 | 84 |
| 2 | 42 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 84 are 2, 3,7.
84 = 22×31×71
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: 2, 3,7,5
.22×32×51×71 = 1260
This shows that the LCM of 84 and 90 is 1260.
How to Calculate the LCM of 84 and 90 Using Common Multiples
The first step in determining the Least Common Multiple of 84 and 90 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 84 and 90:
Lets look at the first ten multiples of these numbers, 84 and 90:
84,168,252,336,420,504,588,672,756,1428 are the first ten multiples of 84.
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 84 and 90, for example, are 1008, 1428, and 1440. 1260 is the least common multiple since it is the smallest.
84 and 90 have an LCM of 1260.
Least Common Multiple of 84 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 84 and 90, than apply into the LCM equation.
GCF(84,90) = 6
LCM(84,90) = ( 84 × 90) / 6
LCM(84,90) = 7560 / 6
LCM(84,90) = 1260
Related Least Common Multiples of 84
Related Least Common Multiples of 90
Frequently Asked Questions on LCM of 84 and 90
1. What is the LCM of 84 and 90?
The LCM of 84 and 90 is 1260.
2. How to find the lowest common multiple of 84 and 90?
To find the lowest common multiple of 84 and 90, we have to get the multip;es of both numbers and identify the least common multiple in them which is 1260.
3. What are the Factors of 84?
Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.
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 84 and 90?Answer:
Least Common Multiple of 84 and 90 = 1260
Step 1: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
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 = 1260 = 2 x 2 x 3 x 3 x 5 x 7
Step 4: Therefore, the least common multiple of 84 and 90 is 1260.